CALCULUS EXAM QUESTIONS AND ANSWERS

CALCULUS EXAM QUESTIONS AND
ANSWERS
derivative of sinx - ANSWER-cosx

derivative of cosx - ANSWER--sinx

derivative of tanx - ANSWER-sec^2x

derivative of secx - ANSWER-secxtanx

derivative of cscx - ANSWER--cscxcotx

derivative of cotx - ANSWER--csc^2x

if the slope of the tangent line is 5/2, then the slope of the normal line is - ANSWER--2/5

derivative of sin-1x - ANSWER-1/root(1-x^2) for -1<x<1

derivative of cos-1x - ANSWER--1/root(1-x^2) for -1<x<1

derivative of tan-1x - ANSWER-1/(1+x^2) for neg. infinity <x < pos. infinity

derivative of cot-1x - ANSWER--1/(1+x^2) for neg. infinity<x< pos. infinity

derivative of sec-1x - ANSWER-1/IxI root(x^2-1) for IxI>1

derivative of csc-1x - ANSWER--1/IxI root (x^2-1) for IxI >1

5 steps for solving a related rates problem - ANSWER-1. identify the variables and
corresponding rates
2. write at least one equation that is a basic relationship between the variables
3. differentiate with respect to t
4. plug in what is know and solve for what is unknown
5. make sure the answer is reasonable

Area of a triangle - ANSWER-A= 1/2bh

Volume of a prism - ANSWER-V=1/3Bh

Area and circumference of a Circle - ANSWER-A=pi r^2
C=2pi r

Volume of a cylinder - ANSWER-V=pi r^2h