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Limits
Derivatives
Applications
Indefinite Integrals
Definite Integrals
100
Find the limit as x approaches -2 of f(x)=x^2-1
3
100
Find the derivative of f(x)=17
0
100
Find y'' if y=e^(2x)
y''=4e^(2x)
100
∫ cos(x) dx
sin(x)+C
100
∫7 dx from x=1 to x=3
14
200
Find the limit as x approaches -3 of f(x)=(x^2-9)/(x+3)
-6
200
Find the derivative of f(x)=-2x^3+25x^2-x+1
f'(x)=-6x^2+50x-1
200
Use implicit differentiation to find y' if x^2+y^2=1
2x+2yy'=0 So y'=-2x/2y=-x/y
200
∫ 4x^3+1 dx
x^4+x+C
200
∫x^2 dx from x=0 to x=1
1/3
300
Find the limit as x approaches 0 of f(x)=(x^2-x+1)/(2x-5)
0
300
Find the derivative of f(x)=5xtan(x)
f'(x)=5xsec^2(x)+5tan(x)
300
Find the x-value that corresponds to the maximum of f(x)=-5x^2+20x-3
f'(x)=-10x+20=0 x=2
300
∫ 2x sec^2(x^2) dx
tan(x^2)+C
300
∫2 sin(x) dx from x=0 to x=pi/2
2
400
Find the limit as x approaches infinity of f(x)=(5x+1)/x
5
400
Find the derivative of f(x)=(3x^2)/sin(x)
f'(x)=(6x*sin(x)-3x^2*cos(x))/(sin^2(x))
400
If y'=(x-2)(x+5)^2, find x-value that corresponds to the minimum of y.
x=2
400
∫ 5 sqrt(1-5x) dx
-2/3*(1-5x)^(3/2)+C
400
∫2/x^2 dx from x=-2 to x=-1
1
500
Find the limit as x approaches infinity of f(x)=(7x^3)/(x^2-3x^2+6x)
infinity
500
Find the derivative of f(x)=sqrt(x^2-5)
f'(x)=(2x)/(sqrt(x^2-5))
500
Find the intervals of concave up and concave down for f(x)=-2x^3+6x^2-3
CU: (-inf,1) CD: (1, inf)
500
∫3x^2 sec(x^3)tan(x^3) dx
sec(x^3)+C
500
∫(x+1)^2 dx from x=1 to x=-1
-8/3