Limits
Inverse Trig
Particle Motion
Antiderivative
Derivative
100
What is limh->0 (f(x+h) - f(x))/h
Derivative of f(x)
100
What is the derivative of arctan(X)
1/(1+x^2)
100
x(t) = t2-6t+5
for what value of t is the velocity of the particle zero?
t=3
100
F'(x)=4x What is F(x)?
F(x)=2x2
100
If F(x)=4x3, what is F'(x)?
F'(x)=12x2
200
Lim x->1 (x2-x-2)/(x2-2x)
2
200
What is the derivative of arccos(x)?
-1/(1-x2)1/2
200
Find the acceleration
S(t) = 2t3 - 2t2 + 4
S"(t)= 12t-4
200
F'(x) = 1/(1+x2) What is F(x)?
tan-1(x)
200
What is the derivative of tan(x)?
Sec2(x)
300
What asymptote is limx->∞ equal to?
Horizontal asymptote
300
What is the derivative of arcsin(x)?
1/(1-x2)1/2
300
f'(x) >0
f"(x) <0
Are the particles increasing or decreasing?
Decreasing
300
find the antiderivative of f(x)= x2ln(x)
((ln(x)x3)/3)-1/9x3+C
300
y=ln(3x+1) what is y'
y'= 3/3x+1
400
What law is used when the limit equals 0/0 or ∞/∞
L'Hopital's rule
400
What is the derivative of arccot(x)?
-1/(1+x2)
400
f'(x) = 0
Is f(x) increasing, decreasing, or stop?
Motion stops (potential turn around)
400
find the anti derivative of f(x)= 2x(x2+4)3
((x2+4)4)/4) + C
400
F(x)= (x3+2x)/(x-1). What is F'(x)?
F'(x)= (2x3-3x2-2)/(x-1)2
500
When does the limit exist?
The limits from the left and right are equal to each other.
500
What is the derivative of arcsec(x)?
1/|x|(x2-1)1/2
500
where is the particle stop?
from 0<x<2
500
find the antiderivative of 1/(5-4x-x2)
1/6(ln(5+x/1-x)+C
500
F(x)= 2cos2(3x)e3x. What is F'(x)
F'(x)=-6e3xcos(3x)(2sin(3x)-cos(3x))