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Calc Exam 3
Formulas and Example Problems
18
Mathematics
Undergraduate 2
04/06/2009
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Term
General Power Rule
 Definition
Integral xn dx=xn+1/n+1 + C
Term
Definition of Natural Logarithmic Function
 Definition
ln x=Integral [x,1] is 1/t dt, assuming x is greater than zero.
Term
3 Properties of the Natural Logarithmic Function
 Definition

1. Domain (0, infinity); range (-infinity, infinity)

 

2. The function is continuous, increasing and one-to-one.

 

3. The graph is concave downward
Term
What is ln (1)?
 Definition
Zero!
Term
What is ln e ?
 Definition
1
Term
What is d/dx[ln x]?
 Definition
1/x
Term
What is d/dx[ln u]?
 Definition
1/u du/dx =u'/u
Term
Differentiate f(x)=ln (x+1)1/2
 Definition
1/2(x+1)
Term
What is d/dx [ln|u|] ?
 Definition
u'/u
Term
∫ 1/x dx
 Definition
ln|x| + C
Term
∫sin u du
 Definition
-cos u + C
Term
∫cos u du
 Definition
sin u + c
Term
∫tan u du
 Definition
-ln|cos u|+C
Term
∫cot u du
 Definition
ln|sin u| + C
Term
∫sec u du
 Definition
ln|sec u + tan u| + C
Term
∫csc u du
 Definition
-ln|csc u + cot u| + C
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