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# CalculusI MATH121

Drexel

GPA 3.63

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This 2 page Class Notes was uploaded by Moshe Swift III on Wednesday September 23, 2015. The Class Notes belongs to MATH121 at Drexel University taught by Staff in Fall. Since its upload, it has received 37 views. For similar materials see /class/212297/math121-drexel-university in Mathematics (M) at Drexel University.

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Date Created: 09/23/15

Calculus 17 Fall 07 REVlEW PROBLEMS 1 Find the domain and range of the function a f96 V962 i 3 W 2 Sketch the graph of the function by translating7 reflecting7 cornpressing7 and stretching the graph of y ay3iv1 b y xE 1 yi f 3 Find a formula for f 1x a f96 3963 i 5 archwapzzo 4 Given that 6 tan l g7 nd the exact values of cos 0 sin 0 cot 0 sec 0 and csc t9 5 Derive the general change of base forrnula loga z logb z loga b Hereagt07 ay 17bgt07 b7 17zgt0 6 Prove that logla flogaz a gt 07 a 31 17 z gt 0 7 Prove that for any positive numbers 1x 31 17 loga z 1 logm 1 Use the result to nd the exact value of log2 81log3 32 8 Solve the equation a 364 5 b logio 1 9 Find lirnan logax Hint Show that lirnan 00 x gt 1 or foo x lt1 10 Find 11min Hint Use l7Hopital7s rule 11 Find 11min Hint Show tha 1 a 12 Find lirnmnjL x 71logm 2 Hint Show that lirnwn x 7 1 logm 2 lirnmnjL 1 m log2 m lirnmnjL inf ln 2 2 13 Find the tangent line to the curve y2 7 z 1 0 at 107 73 in two ways rst by solving for y in terms of z and differentiating and then by implicit differentiation 14 Let y xlB Sketch the graphs of y y and y ldentify critical points7 points of in ection7 and asymptotes for each of them 15 Find the limits using l7Hopital7s rule 71 a 2 b c lin1em lm d lim x 7 lnz2 i sin 410 w lim z sin 1 maoo m 16 Sketch the graph of y mg nd the horizontal and vertical asyrnptotes7 identify points of relative minimum7 relative maximum and in ection points7 intervals of increase7 decrease7 concavity up and concavity down 17 Find the absolute maximum and the absolute minimum values on a given interval for a given function and state where those values occur a JCW l 171l 00 f0 964 426 imam 18 Show that among all rectangles with perimeter p7 the square has minimum area 19 How should two nonnegative numbers be chosen so that their sum is 1 and the sum of their squares is a as large as possible b as small as possible 20 A closed rectangular container with a square base is to have a volume of 2000 cm3 It costs twice as much per square centimeter for the top and bottom as it does for the sides Find the dimensions of the container of least cost

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