Functions, Limits, and Continuity
Derivatives
Integrals
Inverse, Exponential, and Logarithmic Functions
Definitions
100
As x approaches 4, what is the limit of (2x^3-128)/(sqrt(x)-2)
What is 384
100
If f and g are functions such that f(x) = g(x) + k, and k acts as a constant, then f'(x) equals...
What is g'(x)
100
The integral of e^x dx is equal to...
What is e^x + C
100
Find the inverse function of y=9x
What is y=x/9
100
The base of the natural logarithm.
What is e
200
Find the vertical asymptote(s) of the function f(x)=(2x+1)/(x^2-2x-8)
What is -2 and 4
200
If f(x) = g(u) and u = u(x) then f'(x) equals...
What is g'(u) times the quantity of u'(x)
200
The integral of sinx dx is equal to...
What is -cosx + C
200
Differentiate sinx^(x^3)
What is (sinx^(x^3-1))(x^3cosx + 3x^2sinxln(sinx))
200
The slope of the line tangent to a function.
What is derivative
300
A function f(x) is said to be continuous at x=a if...
What is as x approaches a, the limit of the function f(x) equals f(a)
300
True or False. The derivative of [g(x)]^2 is equal to [g '(x)]^2.
What is false
300
The integral of 3cos^(2)5x dx is equal to...
What is (3/2)x + (3/20)sin10x + C
300
Differentiate y=7x(cosx)^(x/2)
What is (7/2)(cosx)^((x/2)-1)(2cosx - x^2(sinx) + xcosxln(cosx))
300
The highest point over the entire domain of a function or relation.
What is absolute maximum
400
Suppose that f(x) is continuous on [a, b] and let M be any number between f(a) and f(b). Then there exists a number c such that...
What is a
400
Find the derivative of 64x^4+5x^2+5x
What is 256x^3+10x+5
400
The integral of sin3x dx is equal to...
What is (-1/3)cos3x + C
400
Differentiate y=x^x
What is x^x(1 + lnx)
400
The theorem of calculus that ensures the existence of a critical point between any two points on a "nice" function that have the same y-value.
What is Rolle's Theorem
500
If F(x)=(x^2-25)/(x^2+x-30), find the value of the limit as x approaches 5.
What is 10/11
500
Find the second derivative of 14x^5+4x^4+x^2+69
What is 280x^3+48x^2+2
500
The integral of (sinx + cosx)^2 dx is equal to...
What is x + sin^(2)x + C
500
Differentiate y=x^(e^x)
What is (x^(e^x - 1))(e^x)(1 + xlnx)
500
An integral which is evaluated over an interval.
What is definite integral
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