Precalculus/ Algebra Review
Limits
Derivatives
Integration
Theorems
100
(Y2-Y1)/(X2-X1), where X1 does not equal X2.
What is the slope of the line?
100
find the vertical asymptotes of f(x)=(2x+1)/(x^2 -2x-8)
What is x=-2, 4
100
1. Find the velocity and acceleration of a particle whose position function is x(t) =t^3-9t^2+24t, t>0
What is a. 3t^2-18t+24; a(t)=6t-18
100
the integral of (5/(x^1/2))dx
What is 10x^1/2 +C
100
f '(c)= (f(b)-f(a))/b-a
What is the mean value theorem
200
y-y1=m(x-x1)
What is the point slope equation of a line.
200
For f(x)=2x^3 +4x^2 +3x-7, show that there exists a number k such that f(k)=20
What is k=3 (see separate sheet)
200
2. Find the derivative of y=e^x at y=e
What is 1/e
200
the integral of (cosx-5sinx)dx
What is sinx+5cosx+C
200
The integral from a to b of f(x)dx= F(b)-F(a)
What is the Fundamental Theorem of Calculus
300
test for even functions
What is the function y=f(x) is even if f(-x)=f(x).
300
Find the value k for which the following limit exists: limit as x approaches 3 of (4x^2 +kx+7k -6)/(2x^2-5x-3)
What is f is continuous on [1,2], the intermediate value theorem states that there exists a number k in the interval (1,2) such that f(k)=20, so f(1)<20<f(2)
300
3. The motion of a particle is given by x=ln(t) and y=t^2-4t. Find the coordinates of the particle when its instantaneous direction of motion is horizontal.
What is (ln 2, -4)
300
the integral of (sec^2 x/ tanx)dx
What is lnabs(tanx) +C
300
If f is continuous on the closed interval [a,b] and k is any number between f(a) and f(b), then there is at least one number c in [a,b] such that f(c)=k.
What is The Intermediate Value Theorem
400
X= (-b±√(b^2-4ac))/2a
What is the quadratic formula?
400
Evaluate the following limit, if it exists: the limit as x approaches 4 of (2x^2 -128)/(x^1/2)-2
What is 384
400
4. Find the derivative of ln(x^4+8)
What is (4x^3)/(x^4+8)
400
the integral of dx/(4-x^2)^1/2
What is sin^-1 x/2 +C
400
Let f be continuous on the closed interval [a,b] and differentiable on the open interval (a,b). If f(a)=f(b) then there is at least one number c in (a,b) such that f '(c)=0
What is Rolle's Theorem
500
(h/2)(a+b)
What is the area of a trapezoid
500
find the equation of tangent lines f(x)= (x-1)/(x+1) at A.(0,-1) and B. (4, 0.6)
What is A. 2x-y-1=0 B. 2x-25y+7=0
500
Find the derivative of ln(x)log(x)
What is (2ln(x))/(xln(10))
500
Find the area of the region between the parabola y=1-x^2 and the line y=1-x
What is 1/6
500
If f is continuous on a closed interval [a,b], then f has both a minimum and a maximum on the interval.
What is the extreme value theorem
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