CALCULUS EXAM #2 STUDY GUIDE
QUESTIONS AND ANSWERS
d/dx [x^e] - ANSWER-ex^(e-1)
d/dx [log(base b) x] - ANSWER-1/x(ln b)
d/dx [log(base b) (f(x))] - ANSWER-f'(x)/f(x)(ln b)
d/dx [tan e^x] - ANSWER-sec^(2) (e^x)(e^x)
volume of a sphere - ANSWER-v= 4/3* pi * r^(3)
d/dx [e^x] - ANSWER-e^x
d/dx [-2/3 e^(-1/2x)] - ANSWER--2/3 e^(-1/2x) * (-1/2)
(lim as h approaches 0) [(f(x+h)-f(x))/h] - ANSWER-Msec (average velocity)
If differentiable - ANSWER-it's continuous.
If continuous - ANSWER-not necessarily differentiable.
sin'x - ANSWER-cosx
cos'x - ANSWER--sinx
tan'x - ANSWER-sec^(2) x
cot'x - ANSWER--csc^(2) x
sec'x - ANSWER-(secx)(tanx)
csc'x - ANSWER--(cscx)(cotx)
arcsic'x - ANSWER-1/sq root(1-x^2)
arccos'x - ANSWER--1/sq root(1-x^2)
arctan'x - ANSWER-1/(1+x^2)
Instantaneous Rate of Change - ANSWER-Slope of tangent line, lim as h approaches 0
When s(t) is increasing - ANSWER-v(t) is positive
QUESTIONS AND ANSWERS
d/dx [x^e] - ANSWER-ex^(e-1)
d/dx [log(base b) x] - ANSWER-1/x(ln b)
d/dx [log(base b) (f(x))] - ANSWER-f'(x)/f(x)(ln b)
d/dx [tan e^x] - ANSWER-sec^(2) (e^x)(e^x)
volume of a sphere - ANSWER-v= 4/3* pi * r^(3)
d/dx [e^x] - ANSWER-e^x
d/dx [-2/3 e^(-1/2x)] - ANSWER--2/3 e^(-1/2x) * (-1/2)
(lim as h approaches 0) [(f(x+h)-f(x))/h] - ANSWER-Msec (average velocity)
If differentiable - ANSWER-it's continuous.
If continuous - ANSWER-not necessarily differentiable.
sin'x - ANSWER-cosx
cos'x - ANSWER--sinx
tan'x - ANSWER-sec^(2) x
cot'x - ANSWER--csc^(2) x
sec'x - ANSWER-(secx)(tanx)
csc'x - ANSWER--(cscx)(cotx)
arcsic'x - ANSWER-1/sq root(1-x^2)
arccos'x - ANSWER--1/sq root(1-x^2)
arctan'x - ANSWER-1/(1+x^2)
Instantaneous Rate of Change - ANSWER-Slope of tangent line, lim as h approaches 0
When s(t) is increasing - ANSWER-v(t) is positive
