Theorems
Derivatives
Integrals
e
Other than e
100
This guarantees the existence of an inverse function.
What is 1 to 1 function
100
f(x)=ln(3x)
What is f'(x)= 1/x
100
⌠(5/x)dx=what?
What is 5ln|x|+C
100
e^lnx=4 Solve for x
What is x=4
100
log base 2 1/8= what?
What is -3
200
Log rule for integration
What is ⌠(1/x)dx=ln|x|+C
200
f(x)=(lnx)^4
What is f'(x)=4(lnx)³/x
200
⌠(x/x²-3)dx=what?
What is 1/2ln|x²-3|+C
200
The derivative of f(x)=e^2x is this
What is f'(x)=2e^2x
200
Solve for x and round to 3 decimal places for 3^2x=75
What is x=1.965
300
Derivative of an inverse function
What is g'(x)=1/f'(x) f'(g(x)) does not=0
300
f(x)=ln(lnx²)
What is f'(x)=1/xlnx
300
⌠(1/√x+1)dx=what?
What is 2√(x-1)+C
300
The derivative of y=ln(1+e^2x)
What is (2e^2x)/(1+e^2x)
300
The derivative of y=5^-4x is this
What is y'=(-4ln5)/(625^x)
400
Limits involving e
What is limit as x->∞(1+1/x)^x
400
f(x)=ln(x+1)²
What is f'(x)=2/(x+1)
400
⌠cot(Θ/3)dΘ=what?
What is 3ln|sinΘ/3|+C
400
The equation of the tangent line to the graph e^(1-x) at (1,1) is this
What is y=-x+2
400
The integral for ∫(3^x)dx is this
What is (3^x/ln3)+C
500
A property of the natural logarithmic function.
What is domain is (0,∞) and the range is (-∞,∞). or The function is continuous, increasing, and 1 to 1. or The graph is concave down
500
f(x)=ln√(4+x)/x
What is f'(x)=-4/x(x²+4)
500
⌠(cos3Θ-1)dΘ=what?
D E E Z N U T Z
500
The derivative of xe^y-10x+3y=0 is this
What is (10-e^y)/(xe^y+3)
500
Evaluate the integral ∫0 to 1 (5^x-3^x)dx
What is (4/ln5) - (2/ln5)
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