Limits
Derivatives
Extrema, Concavity, Increasing and Decreasing
Integrals
Antiderivatives
100
lim x→−3 x^2-x-12/x+3
What is -7
100
Find the derivative of the function: g(x)= 3xsin^2x - x^2 cos x
What is x^1/2 (4-3x) /2(x^2 - 4x)^2
100

Where are the local extrema of f(x)= x3-12x ? 

3x2-12= 3(x2-4)

x= -2( Local Min) , x=2 (Local Max)

100

Integrate: ∫e^x -5x + sec2(x) dx

What is ex - 5/2 x2+ tan(x) + C

100
∫ 15x^4 dx
What is 3x^5+C
200
lim (2+h)^2 - 4/ h h->0
What is 4
200
Find the derivative of the function: y= 5 secxtanx
What is y'= 5 secx (2tan^2x+1) or y'= 5 secx (tan^2x +sec^2x)
200

How many critical points does the function f(x)= x3- 6x2 have

2 critical points

200

∫  sin 4x dx

What is -xcosx + sinx +C

200
∫ -3x^2 dx
What is -x^3 +c
300
lim 3- √t/ t->9 9 - t
What is 1/6
300
y= (2x^2 +5) ^7
What is y'=28x(2x^2 +5)^6
300

Identify points of inflection for the function 

f(x)= 3x3 - 9x2

f'(x)= 9x2-18x

f''(x)= 18x- 18

300

Integrate: ∫1/(3x) dx

What is 1/3 ln x + C

300

∫ (z+2)/z^2 dz

What is ln|z| - 2/z +c

400

lim 1/w - 1/(2w) as w->2 

What is 1/4

400
Find the derivative of the function: f(x)= 7 ^ 1/x
What is f(x)= -ln7*7^1/x / x^2
400

Integrate: ∫1( √x+3) dx

What is 2*sqrt (x+3) +C

400
∫ cotx (sinx) dx
What is sinx+C
500
lim cos [3pi/2 + x]- cos[3pi/2] / x->0 x
What is 1
500
Find the derivative of the function: y= arccos [x/3]
What is y'= -√9-x^2
500

What intervals is the function 

f(x) = 1/12*x4- 1/6*x3 -3x2  concave up? 

(- inf, -2) and (3, inf)

500
Integrate: ∫ x sin x cos x dx
What is (1/2)xsin^2x-(1/4)x +(1/8)sn 2x +C
500
∫ (7t+8)^3 dt
What is (7t+8)^4 ----------- + C 28
M
e
n
u