In this 24 questions- activity, students apply L’Hospital’s Rule to evaluate limits. There are included the following indeterminate forms - 0/0, infinity / infinity, infinite minus infinity and the product of zero and infinity. All functions are included from polynomial to square root, from exponential to log, from trig to inverse trig functions. There are two similar versions of this practice each consisting of two sections. Each section contains three groups of two limits. The problems IN EACH SECTION have THE SAME ANSWER! In section1, two problems have the form 0/0; the next two have the form infinity/infinity and the last two problems have the form infinity minus infinity. In section 2, two problems have the form 0/0; the next two have the form infinity/infinity and the last two problems have the form the product of zero and infinity. ( Not all of the questions require L’Hospital’s Rule (i.e. another valid method could be used) however students are instructed to use only L’Hospital’s Rule to find the limits.) This activity can be used for class work, independent or grouped (groups of 2 or 4). It can be used as an assessment and homework as well. Answer keys are included.

These are 12 challenging practice problems on limits at infinity. Functions included are only exponential, natural logarithms and inverse tangents. The product can be used as independent practice, extra practice, enrichment and homework assignment. The practice sheets have enough room for students to show work. Answer keys are included.

In this 24 questions – collaborative partner activity, students are to find the limits of various functions (polynomial, rational, radical, exponential, logarithmic) as x approaches infinity. To determine the limits, students will need to use a combination of techniques. The limits in this activity can all be found without L’Hopital’s rule. Each partner has his own set of 12 problems. Corresponding partners’ problems are thought carefully so that the answer of each of Partner’s A problems is the same as the answer of its corresponding problem of Partner’s B. almost all of them to be similar examples - limits of functions which are of the same type Students are instructed to show all work and check whether their results match. Answer keys are included.

In this 16 questions - partner activity, students apply L’Hospital’s Rule to evaluate limits. There are included the following indeterminate forms - 0/0, infinity / infinity, infinity minus infinity, zero ⨯ infinity, zero^zero, infinity^zero and 1^infinity. The functions included are polynomial, exponential, logarithmic, trig and inverse trig functions. Each partner has his own set of 8 problems. Partners will use L’Hospital’s Rule to evaluate their first two limits directly. They will need to manipulate to make zero/zero or infinity/infinity and then to apply L’Hospital’s Rule to evaluate the next six limits. ► THE FORM of the limit and THE ANSWER of each of Partner’s A problems are THE SAME as the form of the limit and the answer of each Partner’s B corresponding problem. (Problems A1 and B1 are corresponding, so as problems A2 and B2 and so on). Students are instructed to show all work and check whether their results match. Full solutions are provided.

This engaging and fun activity has the student find the equation to a tangent line at a given value of the variable x. The functions included are polynomial, rational, involving radicals, exponential, logarithmic and inverse trigonometric. Students work independently or in groups of two or three to solve 13 problems. They use a table to find out the syllables corresponding to each of their answers. Then students record the syllables in another table and read the resulting sentence. It is a motivational quotation by the Professor Steven Strogatz about calculus. Student recording sheet and answer keys are included.

This is an engaging and collaborative group activity on finding the absolute extrema of a function (extrema on an interval). The functions included are polynomial, rational, involving radicals, exponential, logarithmic and trigonometric. There are 10 sections - 10 functions. Students work in groups of two, three or/and four. In each section, each member of a group is asked to find the absolute extrema of the given function on a specified closed interval . Thus one and the same function will be examined for absolute extrema at most in four different particular intervals. The collaborative part of this activity is in the initial stage of solving where partners find the first derivative of the given function and determine all the critical values. Students compare their results, find and fix any errors to continue solving in the right direction. They evaluate the function at the critical points found and the end points again having the opportunity to compare their calculations. As a consequence their final (different) answers must be all correct. Student recording sheets with steps that lead to solution and answer keys are included. The product can be also used as an independent/extra practice with 4 different forms and assignment or homework.

This resource contains a total of 16 problems. Students will practice taking the first derivatives of y(x) for each of given implicit functions by implicit differentiation. The packet has 2 worksheets each containing 8 various examples including polynomial, rational, exponential, logarithmic, trigonometric and inverse trigonometric functions. The worksheets can be used as a class practice, for an extra practice or enrichment, an assessment or homework assignment. It can be also used as a partner activity – like that: ⟡ Partner A will solve WS # 1 while Partner B solves WS # 2 , then they swap papers and Partner A will solve WS # 2 while Partner B solves WS # 1 . Once they have completed the work, they compare their results. If there are different answers to one and the same problem, students have to identify and correct any errors. Typed solutions to all of the problems are provided.

This resource contains a total of 24 problems. Students will practice taking the derivatives of some complicated functions by logarithmic differentiation. The packet has 2 worksheets: ⟐ The first worksheet has the students finding the first derivatives of 12 complicated functions using natural logarithms. ⟐ The second worksheet also contains 12 problems of finding the derivatives by logarithmic differentiation as some of the examples are more complex. The worksheets can be used as class practice, for an extra practice or enrichment, an assessment or homework assignment. It can be also used as a partner or group activity – like that: ⟡ Partner A will solve WS #1 (page 1) while Partner B solves WS # 1 (page 2), then they swap papers and Partner A will solve WS #1 (page 2) while Partner B solves WS #1 (page 1). Once they have completed the work, they compare their results. If there are different answers to one and the same problem, students have to identify and correct any errors. Partners continue working through WS # 2 in the same manner with pages 2 and 3 or pages 1 and 2… ⟡ Worksheet # 2 can be used as a group activity ( for groups of 3 as its pages are three and each page contains 4 problems). Full solutions (handwritten clearly) are provided.

This resource contains total of 30 problems. Students will practice higher order differentiation of common and composite functions (with and without the chain rule). The packet has 4 worksheets: ⟐ The first worksheet has the students finding the second derivative of 10 various common and composite functions. ⟐ The second worksheet is finding the third derivative of 6 functions (without using the chain rule). ⟐ The third worksheet is finding the fourth derivative of 6 common functions (without using the chain rule). ⟐ The third worksheet is finding the first four derivatives of 8 composite functions using the chain rule. The worksheets can be used in class for group work or an independent practice, for enrichment, an assessment or homework assignment. Detailed typed answer keys are provided.

This practice worksheet consists of 3 pages and contains 20 problems. Students will practice differentiation of trigonometric functions using the basic properties of derivatives, derivatives of the functions sinx, cox, tanx and cotx, the power, product, quotient and chain rules. There are examples with composite functions where trigonometric function is substituted into exponential and logarithmic functions and examples where exponential function is substituted into trigonometric function. There is one example where the trig function is radicand. Pages 1, 2 and 3 require students to find the first derivative of 17 functions. Page 3 has another 3 problems on finding the equation of the tangent line to a trig function at a given point. Useful for independent /extra practice, enrichment or homework assignment. Typed answer keys are included.

This resource contains total of 20 problems. Students will practice differentiation of common and composite trig functions. The packet has 2 worksheets: ⟐ The first worksheet has the students finding the first derivatives of 10 trig functions using differentiation formulas, the product and quotient rules and the derivatives of the three main trig functions. ⟐ The second worksheet is finding the first derivatives of 10 composite trig functions using the chain rule. The worksheets can be used as class practice, for an extra practice or enrichment, an assessment or homework assignment. It can be also used as a partner activity like: ⟡ Partner A will solve WS # 1 while Partner B solves WS # 2, then they swap papers and Partner A will solve WS # 2 while Partner B solves WS # 1. Once they have completed the work, they compare their results. If there are different answers to one and the same problem, students have to identify and correct any errors. Typed solutions are provided.

This is the second part of my worksheets on Computing Limits. The resource contains total of 16 finite limits. Students will apply the properties of limits and evaluate limits algebraically by substitution, factoring and conjugate methods. The packet has 2 worksheets: ⟐ The first worksheet is solving 8 limits of functions involving radicals (square, cube and fourth roots). ⟐ The second worksheet is solving 8 limits involving functions containing both polynomials and trig expressions or radicals and trig expressions. These problems are more complicated and require using a combination of methods. The worksheets can be used as extra practice, for enrichment, an assessment or homework. It can be also used as a partner activity – like that ⟡ Partner A will solve WS #1 while Partner B solves WS # 2, then they swap papers and Partner A will solve WS #2 while Partner B solves WS #1. Once they have completed the work, they compare their results. If there are different answers to one and the same problem, students have to identify and correct any errors. ⟡ Partner A will solve the first four problems of WS # 1 while Partner B solves the rest four problems of the same WS. Then they swap papers and Partner A will compute the last four limits of WS # 1, while Partner B solves the first four problems of WS # 1. Once they have completed the work, they compare their results. If there are different answers to one and the same problem, students have to identify and correct any errors. Partners continue working in the same way with WS # 2… All answer keys are included.

Students will practice finding vertical, horizontal and slant asymptotes using limits in this activity. There are included rational, involving radicals, exponential and natural logarithm functions. Students will work through 7 sections (or less if preferred). There is a function given in each section and differentiated instructions to each of the partners. In each section they share their work like this – Partner A finds all the vertical asymptotes of the given function while Partner B finds the slant asymptote of the same function. In the next section Partner B finds the vertical asymptotes of another function while Partner A finds the slant. There are sections where one of the partners is asked to find the horizontal asymptotes and the other partner – the vertical. The last section asks Partner A to find the left horizontal asymptote and Partner B – the right horizontal asymptote of a function. Students recording sheets are specially designed for this activity with HINTS and rooms to show work. Partners have to record all their answers in a table on a partners’ response sheet provided. Answer key is included.

This resource contains total of 16 limits. Students will apply the properties of limits and evaluate the limits algebraically by factoring and substitution methods. They will also need to use basic trig limits and identities to solve the limits of trig functions. The limits in this activity can all be found without L’Hopital’s rule. The packet has 2 worksheets: ⟐ The first worksheet has the students solving 8 limits of rational functions. ⟐ The second worksheet is solving 8 limits of trigonometric functions. The worksheets can be used as extra practice, for enrichment, an assessment or homework. It can be also used as a partner activity – like that: Partner A will solve WS # 1 while Partner B solves WS # 2, then they swap papers and Partner A will solve WS # 2 while Partner B solves WS # 1. Once they have completed the work, they compare their results. If there are different answers to one and the same problem, students have to identify and correct any errors. All answer keys are included.

This is an engaging practice that investigates infinite limits both graphically and algebraically. Students are asked to graph 8 functions and evaluate 24 limits (right and left-hand limits included) based on these graphs. Then students are asked to prove 11 equalities that is to check whether 11 infinite limits are evaluated correctly. Students are provided with rooms to show work and coordinates grids where each axis labeled using an appropriate scale as dictated by the problem. All the graphs are presented in the answer keys. The resource can be used for class work, as an individual practice or homework assignment.

Students will apply L’Hospital’s Rule to evaluate limits. The resource contains practice problems classified into 4 categories according to the indeterminate forms – 0/0, infinity / infinity, zero ⨯ infinity and infinity minus infinity. There are 10 problems for each category and else 10 extra review problems(total of 50 limits). The functions included are rational, exponential, logarithmic, trig and inverse trig functions. The product can be used in class for cooperative learning , as a partner or a group activity, independent (extra) practice, enrichment or homework assignment. Full solutions (handwritten clearly) are provided.

These are 6 Christmas themed task or station cards grouped with 10 to 15 similar problems per card. There are a total of 81 carefully chosen problems concerning the following applications of the derivatives: ❄finding critical points (Card A - 15 problems) ❄ determining intervals of increasing and decreasing (Card B - 15 problems) ❄ finding local extrema (Card C - 15 problems) ❄ finding absolute extrema on the specified intervals (Card D - 10 problems) ❄ finding inflection points (Card E - 14 problems) ❄ determining intervals of concavity (Card F - 12 problems) The functions included are rational, radical, trigonometric, inverse trigonometric, exponential, and logarithmic (common and composite functions). The cards can be used individually or with groups. Student recording sheets are included. Detailed answer keys/solutions (handwritten clearly) are included.

This is an engaging card sort activity for studying the intervals of concavity and inflection points of given functions. The functions (common and composite) include polynomials, radical, exponential, logarithmic, trigonometric and inverse trigonometric expressions. They are specially selected so that each function has not more than one inflection point. Activity Directions: Students determine the intervals of concave up/concave down and the inflection points of each of 12 given functions. They are also given 16 cards each with a statement written on it. The statements concern the concavity and inflection points of the given functions and are true or false. Partners are asked to use their studies on the functions to verify the statements and sort the cards into two groups - “TRUE” and “FALSE”. Thus students do comparative analysis of the functions. This product can be possibly used as an independent practice, as a partner or a group activity (groups of 3 and 4). Student recording sheet and all answer keys are provided.