Derivatives
Anti-Derivatives
Series and Sequences
Taylor and MacLaurin Series
Graph Analysis of Derivative Functions
100
the derivative of f(x)= sin(x)
What is f '(x)= cos(x)
100
the anti-derivative of f(x)= cos(x)
What is sin(x) + c
100
2, 5, 7, 10, 12, 15, ____
What is 17
100
=1-(1/2!)x^2+(1/4!)x^4-(1/6!)x^6+....
What is the Taylor Series for f(x)=cos(x) about x=0.
100
f(x) has a _______ at x=2 because f '(x)= 0 and changes from positive to negative
What is a max or local max
200
the derivative of f(x)= sec(x)
What is f '(x)= sec(x)tan(x)
200
the anti-derivative of f(x)= 4x^3 + 7x^2 + 18x - 2
What is x^4 + 7x^3 / 3 + 9x^2 - 2x + c
200
4, 10, 20, 34, 52, ____
What is 74 <2(x^2)+2>
200
= (1/1!)x=(1/3!)x^3+(1/5!)x^5-(1/7!)x^7+.....
What is the Taylor Series for f(x)=sin(x) about x=0.
200
f(x) has a _______ at x=2 because f '(x)= 0 and changes from negative to positive
What is a min or local min
300
the derivative of f(x)= 4x^3 − 3x^2 + 2x − 17
What is f '(x)= 12x^2 − 6x + 2
300
the anti-derivative of f(x)= 1/1+x^2
What is tan^-1(x) + c
300
a geometric series is given below 34, 51, 68, 85, 102, 119 the common ratio (r) is
What is 17
300
f(a)+(f'(a)/1!)(x-a)+(f"(a)/2!)(x-a)^2+(f'''(a)/3!)(x-a)^3+...
What is the formula for a basic Taylor Series
300
the ________ derivitive determines the concavity of f(x)
What is the second dervivitive
400
the derivative of f(x)= cos(x)sin(x)
What is f '(x)= (cos(x))^2-(sin(x))^2
400
the anti-derivative of f(x)= -csc(x)^2
What is cot(x) + c
400
a p-series is given below: 1/n^p = 1/1^p + 1/2^p + 1/3^p + ... where p>0 this series converges when p(< or >)1
What is p>1
400
the first four nonzero terms of the Maclaurin Series for f(x)= sin(x)
What is sin(x)= x − x^3/ 3! + x^5/ 5! - X^7/ 7! + ...
400
True or False: All intervals above the x axis represent increasing slopes
What is false
500
the derivative of f(x)= sin(x)/cos(x)
What is f '(x)= (cos(x))^2+(sin(x))^2/(cos(x))^2
500
the anti-derivative of f(x)= x^2sin(x) using integration by parts
What is -x^2 cos(x) + 2xsin(x) + 2cos(x) + c
500
an alternating series test must meet the following requirements
What is 1) alternates, 2) terms go to 0, 3) An+1<An
500
the first four nonzero terms of the Maclaurin Series for f(x)= xe^x
What is x (1 + x/ 1! + x^2/ 2! + x^3/ 3!) or (x + x^2 + x^3/ 2! + x^4/ 3!)
500
f(x) is concave ___ when f '(x) is increasing
What is concave up
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