Limits
The limit of x^2 + 5x - 8 as x approaches 12
What is 196?
derivative of 5x^2
What is 10x?
The integral of 3x^2
What is x^3 + C?
Given the position function f(x)=x2, the velocity at x=4 is
What is 8?
The instantaneous rate of change of the function at a or the slope of the tangent line at a.
What is the derivative of f at a?
The limit of (5+2x)/(1-2x) to negative infinity
What is 5?
The derivative of the integral of sin(x) from 2 to x2
What is 2xsin(x2)?
The integral of sin(x) from -π to π
What is 0?
Given the position function x(t)=3x3-15, the speed at t=4 is
What is increasing?
A number c in an open (a,b) interval where the derivative is zero or does not exist.
What is Critical Number c?
The limit of sin(17x)/x as x approaches 0
What is 17?
The slope of 1/(x2+3) at x=2
What is -4/37?
The integral of sin(πx)-8x3 from 0 to 1/2
What is -1/8 + 1/π?
The volume of a ballon is increasing at a rate of 27π in3/sec. When the radius is 3 inches, the rate of change of the radius is
What is 3/4 in/sec?
The name of this theorem: (f(b)-f(a))/(b-a) = f'(c)
If the function is differentiable and continuous, there is some c, b < c < a, where f'(c) = the slope of the secant line of the function
What is mean value theorem?
The limit of the piecewise function: f(x)= x+3, x>2 12(x^2)-42, x< or = 2 as x approaches 2
What is DNE?
The derivative of x2(x-4)4
What is 4x2(x-2)3+2x(x-2)4?
The integral of 1/(√(4-x2))
What is sin-1(1/2x)+C?
Two cars leave town at the same time. Car A heads due north at 80 km/hr and Car B travels east at 60 km/hr. The rate at which the distance between the cars is increasing at t=3 is
What is 100 km/hr?
The limit of (e^x - ln(e) +6)/(5x-2) as x approaches 0
What is -3?
Where does f(x)= esinx have a horizontal tangent?
What is π/2 and 3π/2?
The integral of 5/(1-x)
What is -5ln(1-x)+C?
This man's first law uses related rates to state that an object with no force acting on it will move in a straight line at a constant speed. (He is often considered the father of calculus)
Who is Sir Isaac Newton?