# Calculus Questions

## Transcribed Text

1. (a) Give a clear and concise delinition of L. (b) Evaluate the following limits: 2r 1 5 2:15 I+I i) =+1 ii:) lim (2-546'-) 3-2 = 2. (a) Cive a clent and concis definition the statement "J(x) continuous at the point t= (b) Find value K that the function f(x) is contimous at r = = wheme iss" (c) Clearly and concisely state the result known as the Extreme Value Theorem for continuous functions 3. (a) Let A/ i(2- A)-1(2) for /(x) 3x r2 Calculate lim AJ h tan(2.2) (h) Evaluate lim (c) Evaluate lim 4. (a) Give clear and concise definition of the derivative of function. What does the deriva live of a function al single point vell us aboubits graph al that point? (h) U=e the definition of derivative to find 1'(2) for fix) = 3x 7 (c) Find the equation of the tangent line the graph of the function ((x) 3x - 2" at the point (2,2) What the area the triangle formed b this tangent line and the positive co-ordinate axes? 6. Leu y(x) be delined implicitly by he quation any sty. Find y in torms of and y. 8. Let /(x) (a) What the domain of the function /(x) ? (b) Use logarithunic differentiation to find l'(x) (c) For what values of P'x) =07 0 Use L'Hopital's rule find the following, limits tan z x-sing 5) 12. Sketch the graph of the curve y Besure to find the intervals of increase, decrease and constant concavity and all local extremes and inflection points 1. (a) Give elear and concial definition of (b) What are the following limits? 2x-5 2x-5 lim T-1 x-1 16x² 5 ie) & x²) vi) lim 2x2-1 2. (a) Civonelear and poncine definition ofthe /(x) continuous al the point z=c", (b) Give clear and cono definition ofte statement /(x) contannons on the closod interval Ja, (c) compound /(x) j(x) Let the function be defined by i. Calculate Lin /(x) and [(x). ii. For what value of Kis the function /(x) s continuous nt: & 3. (A) Let A/ h) (1) for 2x Caleulato sin(2x) (b) Evaluate lime sin(3x) (c) Evaluate 4. (a) Give cloar and poncise delinition uf derivative uf Junction al a point. What dous the value c the derivative of function at single point tell us about its tangent line at that point? (b) Use the delinition of derivative wo lind J'(1) for /(x) -1+22+1 (c) Find the equation of the tangent line of the graph of the function /(x) P -2x+ at the point 7). Graph this tangent line and find the prea of the triangle formed by this tangent line and the co ordinate axes. 5. Find the derivativ ves of the following functions. Simplify your answers b) VI-I 0 "3-1 clas (x 1) ne" 1)+ 7. Let s(2) be delined implicitly by Lie equation t2 12 16. (a) Findy terms of and y (b) Findy terms of a andy 9. Usel Hopital's rule or otherwise to find the following limits: sin2: a) lim 1 11. Sketch the graph of the curve 8 3x2 2. Be sure to find the intervals increase, docroase stant coneswity and coordinates local extremes inflection pointa Alno indicate the number and valuos of any x interecpia (accurato to 2 docimal they ano not all 1. (a) Give clear and concise definition of lim (h) Ecaluase the following limits: in) lim 2 5 lim P-2 m² 81°-2 2. (a) Give clear and concise definition of the statement "/(x) continnons at the point T=c" (b) Finda value K so that the function (ix) continuous at x - where set. (c) Clearly and concisely state the result known de Lie Intermodiale Value Theorem for continuous functions. A7 3. (a) Let A/ 13 4) r(3) for /(z) 3x 25 Calculate and tan(2x) (b) Evaluate lim (c) Evaluate 4. (a) Give clear and concise definition of the derivative of function What does the deriva function at. single point cell na about ita graph at that peint? (b) Use the definition of derivative to ind /(3) for (x) 3a 2 (e) Find the ormation the tangent line of the graph the function j(z) 3x the point (3.0) What sthe area the trianglo formed by thistongent lino and the positivo co-ordinale axes? 5 (a) Find the equation of the tangent line to the curve T³ 2xt at its point of inflection (b) Let y(x) be defined implicitly by the equation 2y y. Find, y al the point (2,2). 7. Lef /(x)= 1)(z (a) What is the domain the function f(x) (b) Use dilleventiation to lind l'(x) (c) For what values of in the domain of ((x)=1 9. Use the following limits: state result known asthe Moan Value Theorem for differentinble Find salislies conclusion of be for ((x) the

## Solution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

\$50.00 for this solution

PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

### Find A Tutor

View available Calculus Tutors

Get College Homework Help.

Are you sure you don't want to upload any files?

Fast tutor response requires as much info as possible.