Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
A series of calculus problems focusing on limits, derivatives, and applications of calculus. It includes problems on evaluating limits using graphs, computing derivatives of various functions, applying the mean value theorem, implicit differentiation, and optimization problems. The document also covers linear approximation and sketching graphs based on given conditions. It is designed to test and enhance understanding of fundamental calculus concepts and problem-solving skills. This resource is suitable for students studying calculus at the high school or university level, providing a comprehensive review of key topics and techniques. The problems are presented in a clear and structured manner, making it easy for students to follow and practice. The document serves as a valuable tool for exam preparation and reinforcing calculus knowledge.
Typology: Exams
1 / 6
This page cannot be seen from the preview
Don't miss anything!
Problem 1: (5 points each) a. Use the graphs to evaluate the following limits.
f(x) \
b. Compute the limit, show and justify your steps.
r+ lim (^).
X—> -7^ WL%^ L^ R^ o
problem 2: (4 points each) For each function £ (x), compute the derivative f'(x). No need to simplify your answers. //,' f(x) = sinh(ln(x)) ] = S —l—— TSR (IRGY Y ¢ gos (^2) (\vxux
f(x) =47 - 3x%)? Tzl (=
COERUI s (YU y +1D)
f(x) = cos(x?) e?* PRSI0 0+ (^25) (2255 F Los G
changed ged w when the side i lengths are 2 cm? Provide units in your —————^ answer. Y=Yk p= d
Problem^ 6:^ (10^ points)^ For^ the^ function^ f(x)^ =^ xIn(x)^ ... a. Find^ the^ critical^ numbers.^ e : LN^ O^ =D b. Determine^ the^ intervals^ on^ which^ f(x)^ is^ increasing and^ decreasing.^ o U^ e =^ = e^ © |
xC ————+ (^) > | 0 a \ww.m TeroS (^). (^) () OO NG+, ) (0N
Problem^ 7:^ (10^ points)^ Answ a. Use^ the^ closed^ interval^ method^ to^ fin interval^ [—%,n]. b. A box^ has^ asquare^ base,^ an^ open^ top,^ and a volu er^ ONLY^ ONE^ of^ the following^ questi d the^ maximum ons: and^ minimum^ values of f(x)^ =^ 1+^ cos^ (x) onthe i i^ box that^ requires me^ of^32 m’.^ Find the^ dimensions of^2 q the^ least^ amount^ of^ material. 290 ?)37. ( =
