901 Quizzito

Suppose that g is a function with the following two properties: g(-x)=g(x) for all x, and g'(a) exists. Which of the following must necessarily be equal to g'(-a)?

-g'(a)

The acceleration at time t>0 of a particle moving along the x-axis is a(t)=3t+2 ft/sec^2. If at t=1 seconds the velocity is 4 ft/sec and the position is x=6 feet, then at t=2 seconds the position x(t) is

13ft

The graph of the function f(x)=2x^5/3 - 5x^2/3 is increasing on which of the following intervals.

1<x and x<0 -- I and III only

The approximate value of y=(3+e^x)^1/2 at x=0.08, obtained from the tangent to the graph at x=0, is

2.02...

The area of the first quadrant region bounded above by the graph of y=4x^3 +6x-1/x between the values of x=1 and x=2 is

24-ln2...

If f'(x)=ln(x-2), then graph of y=f(x) is decreasing if and only if

2<x<3

What is the average (mean) value of 2t^3-3t^2+4 over the interval -1≤t≤1

3

d/dx(lne^3x)=

3...

What is limx->∞ (9x^2+2)^1/2/4x+3

3/4

A leaf falls from a tree into a swirling wind. The graph at the right shows its vertical distance (feet) above the ground plotted against time (seconds). According to the graph, in what time interval is the speed of the leaf the greatest?

3<t<5

Let the first quadrant region enclosed by the graph of y=1/x and the lines x=1 and x=4 be the base of a solid. If cross sections perpendicular to the x=axis are semicircles, the volume of the solid is

3pi/32

Use a right-hand Riemann sum with 4 equal subdivisions to approximate the integral -1,3∫|2x-3|dx

8

Let F be the function given by F(x)=0,x∫2/(1+t^4)dt. Which of the following statements are true?

F(2)<F(6) and F''(0)=0 -- II and III only

The slope field for a differential equation dy/dx=f(x,y) is given in the figure. The slope field corresponds to which of the following differential equations?

dy/dx=sinx

If g'(x)=2g(x) and g(-1)=1, then g(x)=

e^(2x+2)

A relative maximum of the function f(x)=(lnx)^2/x occurs at

e^2

Let f(x)=lnx+e^-x. Which of the following is TRUE at x=1?

f is increasing

2,6∫(1/x+2x)dx

ln3+32

For x≠0, the slope of the tangent to y=xcos equals zero whenever

tanx=1/x

An equation of the line tangent to the graph of y=x^3+3x^2+2 at its point of inflection is

y=-3x+1

∫cos(3-2x)dx

-1/2sin(3-2x)+c...

The function F is defined by F(x)=G[x+G(x)] where the graph function G is shown at the right. The approximate value of F''(1) is

-2/3...

If y=cos^2 (x)-sin^2 (x), then y'=

-4(cosx)(sinx)

Water is flowing into a spherical tank with 6 foot radius at the constant rate of 30pi cu ft per hour. When the water is h feet deep, the volume of water in the tank is given by V=(pi*h^2/3)(18-h). What is the rate at which the depth of the water in the tank is increasing at the moment when the water is 2 feet deep?

1.5 ft per hr

What is lim x->1 (x)^1/2 -1/x-1?

1/2

If f(x)={x^2 +4 for 0≤x≤1, 6-x elsewhere then 0,3∫f(x)dx is a number between

10 and 15

An equation for a tangent line to the graph of y=arctan(x/3) at the origin is:

x-3y=0

∫(x-2)/(x-1)dx=

x-ln|x-1|+c