Limits
The value of lim as x approaches 2 of (x2-4)/(x-2).
What is 4?
Differentiate f(x)=x3+2x
What is 3x2+2?
If f'(x)>0, what can you say about f(x)?
What is the function is increasing where f'(x)>0?
The indefinite integral of xdx.
What is (1/2)x2+c?
What does the integral from a to b of v(t) dt represent?
What is displacement? or net change in position?
True or false: if the limit of f(x) exists as x approaches a, then f(a) must be defined.
What is false? The existence of a limit does not require the function to be defined at that point.
The derivative of sin(x)*cos(x)
What is cos2(x)-sin2(x)?
A ladder 10 ft long is leaning against a wall. If the base is sliding away at 1 ft/sec, how fast is the top falling when the base is 6ft from the wall?
What is -0.75 ft/s? (Use pythagorean theorem: related rates/differentiate x^2+y^2=100)
The value of the integral from 0 to 2 of (x2+1)dx.
What is 14/3?
Find the area between y=x and y=x2 on [0,1].
What is 1/6?
The value of the limit as x approaches 0 of sin(3x)/x.
What is 3?
The derivative of (x2+1)5.
What is 10x(x2+1)4?
The critical points of f(x)= x3-3x.
What is x=-1, 0, 1?
The u for the integration of x*(x2+1)1/2dx
What is u = x2+1?
Find the volume of the solid generated by rotating y = sqrt(x) between x=0 and x=4 about the x-axis.
What is 128pi/5? (disk method).
The value of the limit as x approaches positive infinity of (3x2+5x+1)/(x2-4)
What is 3?
The derivative of (x2+1)/x?
What is (x2-1)/x2?
You are building a rectangular garden against a wall. You have 40 meters of fencing to enclose three sides (the fourth side is along the wall). What expression gives the area of the garden in terms of the width x, where x is perpendicular to the wall?
What is A(x)= x(40-2x)? The fence encloses 2 sides of length x and 1 side of length y so 2x+y=40, solve for y and plug that into area = x*y.
The antiderivative of (2x)/(x2+1)
What is ln(x2+1)+C?
Find the total distance traveled by a particle with v(t)=t2-4 over [0,3]
What is 5? Integrate with absolute value for total distance.
Limit as x approaches 0 of |x|/x
What is DNE? The left hand and right hand limits do not match.
The derivative of x2tan(x).
What is 2xtan(x)+x2sec2(x)?
A cone-shaped tank is draining. The height and radius are related by r=(1/2)h. If the volume is decreasing at 3 m³/min when the height is 4 m, how fast is the height changing?
The result of the integration of xexdx
What is xex-ex+c? (from your quiz yesterday)
Set up but do not evaluate the integral for volume when the region between y=x and y = x2 is rotated about the y-axis.
What is the integral from 0 to 1 of 2 pi x(x-x2)dx? Use cylindrical shells with height x-x2 and radius x.