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Prerequisites
Limits & Continuity
Derivatives
Definitive Integral
Differential Equations
100
Write an equation for a line with a slope of -3 and y-intercept of 3.
y = -3x + 3
100
Find the average rate of change of f(x)=1+sinx over the interval [0,π/2]
2/π
100
What is the derivative of y = (2x+1)/(2x-1) ?
4/(2x-1)^2
100
1 ∫(8x^3-12x^2+5)dx 0
3
100
∫ t dt/t^2 + 5
(1/2)ln(t^2+5) +C
200
Is y = x ^ 1/5 symmetric about the y - axis, origin, or neither?
Origin.
200
What is the limit of (x+sinx)/(x+cosx) as x approaches infinity?
1
200
Find all the values of x for which y = ln x^2 is differentiable.
For all values x, x is not equal to 0.
200
2 ∫(2/y+1)dy 0
2ln3
200
∫(e^3x)sinx dx
((3sinx)/10 - (cosx)/10)e^3x + C
300
Write an equation for a line that goes through (4,-2) and has an x - intercept of -3.
y = -2x/7 - 6/7
300
What is the limit of e^x sinx as x approaches infinity.
0
300
What is the second derivative of x^3+y^3=1 ?
-2x/y^5
300
Solve for x. x ∫(t^3 - 2t + 3)dt = 4 0
x is approximately 1.63052 or -3.09131
300
Find an integral equation such that dy/dx = sinx^3 and y=5 when x=4
y = x ∫ sint^3 dt + 5 4
400
Is y = (x^4 +1)/(x^3 -2x) even, odd, or neither?
Odd.
400
What is the limit of x^3 - 2x^2 + 1 as x approaches -2?
-15
400
Find an equation for the tangent and normal line to y = 4 + cotx - 2cscx at x=π/2.
Tangent Line: y = -x + π/2 + 2 Normal Line: y = x - π/2 + 2
400
Find dy/dx. 2x ∫(1/t^2 + 1)dt x
(2/4x^2 - 1)-(1/x^2 + 1)
400
Find the amount of time required for $10,000 to double if the 6.3% annual interest is compounded annually and continuously.
Annually: 11.3 years Continuously: 11 years
500
What is the domain and range of y = 2sin(3x+π)-1?
Domain: All real numbers. Range: [-3,1]
500
Find the slope of the curve y = x^2 - x - 2 at x=a
2a-1
500
Let y = (e^x + e^-x)/2. Find the first and second derivative.
First derivative: (e^x - e^-x)/2 Second derivative: (e^x +e^-x)/2
500
Let f be a differentiable function with the following properties: i. f'(x) = ax^2 + bx ii. f'(1) = -6 and f"(x) = 6 iii.2 ∫f(x)dx=14 1 Find f(x).
f(x)=4x^3-9x^2+20
500
A population P of wolves at time t years (t is greater than or equal to 0) is increasing at a rate directly proportional to 600 - P, where the constant of proportionality is k. If P(0)=200, find P(t) in terms of t and k, and find the limit of P(t) as t approaches infinity.
P(t) = 600 - 400e^-kt limit = 600