Unit 1/2
What is the limit as x approaches -1 (2x2+3x+1)/(x2-2x-3)
what is 1/4
Find the limit as x approaches 0 (ex-x-1)/(cosx-1)
what is -1
Let g be a twice differentiable, increasing function of t. If g(1)=4 and g(4)=28, what must be true on the interval 1<x<4?
A) g'(t)=0
B) g'(t)=8
C) g''(t)=0
D) g''>0
What is B) g'(t)=8 for some t on interval
Which of the following is a solution to the differential equation xy'-3y=6
A) y=x2+2
B)y=3x2-2
C) y=5x3-2
D)y=7x3+2
What is C) y=5x3-2
Find the derivative of h(x)=f(x)*g(x)
f(x)=lnx
g(x)=x3+1
Product rule:
What is h'(x)=1/x(x3+1)+ln(x)(3x2)
Use linear approximation to approximate when x=1.004. Let f(x)= 1/x and use x=1 to approximate.
L(1.004)=f(1)+f'(1)(1.004-1)
What is L(1.004)=0.996
Find the anti derivative of f(x)= (6x2-4x+3)/(x)
What is 3x2-4x+3ln|x|+C
f(x)=2x+1 is defined on the interval [1,5].
What is the average value of the function on this interval?
What is 7?
Find derivative of f(x)=(2x-3)4*(x2+x+1)5
Chain rule:
What is f'(x)=8(2x-3)3*(x2+x+1)5+5(x2+x+1)4*(2x+1)*(2x-3)4
Find absolute maximum of the function given on the interval [2,4].
f(x)=x3-6x2+9x+1
What is f(4)=5
f(x)=x4-4x3+6x2+1
When does the point of inflection occur?
A) x=1
B)x=-1
C)x=0
D) There are no points of inflection
What is there are no points of inflection (never changes concavity)
Solve the differential equation dy/dx=2x given that y(1)=3.
What is y=x2+2
Find the derivative of f(x)=((x2+1)/(x2-1))3
Chain+quotient rule:
What is f'(x)=(-12x(x2+1)2)/(X2-1)4
f(x)= x2g(h(x)) where g(5)=3, g'(5)=-2, h(2)=5, and h'(2)=4. FIND f'(2).
A) -20
B)-32
C)20
D)32
What is -20.
Which of the following is equivalent to the integral of cos(3x)sin5(3x)dx?
A) 1/3 integral cos udu multiplied by 1/3 integral sin5udu, where u=3x
B) Integral cos(3x)dx multiplied by integral sin5(3x)dx
C) 1/3 integral u5du, where u=sin(3x)
D) Integral u5 du= where u=sin(3x)
What is C) 1/3 integral u5du, where u=sin(3x)
This integral represents the area between the curves y=sinx and y=cosx on the interval where cosx is greater than or equal to sinx:
What is the integral of (cosx-sinx) on the interval (0,pi/4)
Find derivative of g(x) which is the inverse function of f(x).
f(x)= 4/1+x2, g(2)=x, domain is x greater than or equal to 0.
g'(2)=1/f'g(2)
what is g'(2)=-1/2
A balloon is rising vertically at a rate of 3 meters per second. A person is standing 40 meters away from the point on the ground directly below the balloon. How fast is the distance between the person and the balloon increasing when the balloon is 30 meters high? (Hint: the person isn't moving horizontally).
what is 1.8 m/s
A particle moves along a line with position s(t)=t3-6t2+9t. Find when the particle is moving to the left.
What is between the interval (1,3).
A region is bounded by the curves y= sqrt of x, y=0, and x=4. Give the integral expression and then find the volume of the solid formed when this region is rotated about the line y=2.
What is pi times the integral of [(2)2-(2-sqrt of x)2]dx from b=4 and a=0? And what is (40pi)/3?