Limits
Differentiation
Applications of Derivatives
Integration
Miscellaneous
100
The limit as x approaches infinity of (3x + 3) / (4x-7)
What is 3/4 ?
100
The derivative of f(x) = cosx
What is -sinx?
100
f"(x) > 0
What is concave up?
100
The integral of xdx
What is (x^2)/2 + C ?
100
Isaac Newton and Gottfried Leibniz
Who is credited for inventing calculus?
200
The limit as x approaches infinity of 1/x
What is 0 ?
200
The derivative of f(x) = 3x^2 + 6x + 5
What is 6x + 6 ?
200
f'(x) goes from positive to negative
What is a maximum?
200
The integral of (2x-3)dx
What is x^2 + 3x + C ?
200
f'(x)g(x) + g'(x)f(x)
What is the product rule?
300
The limit as x approaches 1 of (2x^2 - 4x) / (6x - 2)
What is -1/2 ?
300
The derivative of f(x) = -e^-x
What is e^-x ?
300
(end position) - (beginning position)
What is displacement?
300
The integral of 1/x dx
What is ln(x) + C ?
300
f'(g(x)) * g'(x)
What is the chain rule?
400
The limit as x approaches 1 of (x^2 - x) / (x^3 - x)
What is 1 ?
400
The derivative of f(x) = -x^-2 + 3x
What is 2x^-3 + 3 ?
400
f'(c) = ( f(b) - f(a) ) / (b - a)
What is the Mean Value Theorem?
400
The integral of x(x^2+1)^3 dx, from -1 to 1
What is 0 ?
400
The derivative of x^2 + y^2 = 30
What is -x/y ?
500
The limit as x approaches 3 of (x^2 + 9x +9) / (x^2 - 9x -9)
What is 5/3 ?
500
The derivative of f(x) = (4x-3)(2x+4)
What is 16x+10 ?
500
f'(c) = 0 and f"(c) > 0, then a f(x) has a min at x = c ; f'(c) = 0 and f"(c) < 0, then a f(x) has a max at x = c
What is the 2nd Derivative Test?
500
The integral of (6x^2+3x-2) dx, from 2 to 4
What is 118 ?
500
Sign change on f"(x)
What is point of inflection?
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