Properties of ln Functions
ln Function Derivatives
ln Function Integrals
Properties of Exponential Functions
Derivatives and Integrals of Exponential Functions
100
ln(1)=
What is 0
100
d/dx[ln(x)]=
What is 1/x, x>0
100
$ 1/x dx =
What is ln|x| + C
100
The domain of f(x)=e^x The range of f(x)=e^x
What is (-Infinity,Infinity) (0,Infinity)
100
d/dx(e^x)=
What is e^x
200
ln(ab)=
What is ln(a) + ln(b)
200
d/dx ln(u) =
What is u'/u, u>0
200
$ 1/u du =
What is ln|u| + C
200
The function of f(x) = e^x is (Describe the function)
What is continuous, increasing, and one-to-one on its entire domain.
200
d/dx(e^u)=
What is (e^u)(du/dx)
300
ln(a^n)=
What is n ln(a)
300
d/dx[ln(2x)]=
What is 1/x
300
$ 2/x dx =
What is ln(x^2)+C
300
$ e^x dx =
What is e^x + C
400
ln(a/b)=
What is ln(a) - ln(b)
400
d/dx[x ln(x)]=
What is 1+ln(x)
400
$ 1/(4x-1)dx =
What is (1/4) ln|4x-1|+C
400
lim(x->-Infinity) e^x = lim(x->Infinity) e^x =
What is 0 Infinity
400
$ e^u du =
What is e^u + C
500
Definition of the natural logarithmic function.
What is ln(x) = $(1 to x) 1/t dt, x>0
500
d/dx[(ln(x))^3]=
What is 3[ln(x)]^2 * 1/x
500
Int (3x^2 + 1)/(x^3 + x) dx =
What is ln|x^3 + x| + C
500
Definition of the natural exponential function
What is y=e^x if x=ln(y)
500
$(0 to 1) (e^x)/(1 + e^x) dx =
What is 0.620
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