Calc Answers

If f(x)=-x^3+x+1/x, then f'(-1)=

-3

What are all values of K for which S k, -3 x^2 dx=0?

-3

If the function F is continuous for all real numbers and if f(x)=x^2-4/x+2 when x does not equal -2, then f(-2)=

-4

lim theta>0 1-costheta/2sin^2theta is

1/4

If f(x)=ln|x^2-1|, then f'(x)=

2x/x^2-1

Let F be a function defined for all real numbers x. If f'(x)=|4-x^2|/x-2, then F is decreasing on the interval

(-infinity,2)

At what point on the graph of y=1/2x^2 is the tangent line parallel to the line 2x-4y=3?

(1/2,1/8)

What are all values of X for which the function F defined by f(x)=(x^2-3)e^-x is increasing?

-1<x<3

If x^2+y^2=25, what is the value of d^2y/dx^2 at the point (4,3)

-25/27

d/dx cos^2(x^3)=

-6x^2sin(x^3)cos(x^3)

If x^2+xy=10, then when x=2, dy/dx=

-7/2

S xsin (2x)dx=

-x/2cos(2x)+1/4sin(2x)+C

If f(x)=(x-1)^2sinx, then f'(0)=

1

At time t_>0, the acceleration of a particle moving along the x-axis is a(t)=t+sint. At t=0, the velocity of the particle is -2. For what value T will the velocity of the particle be 0?

1.48

The expression 1/50(radical 1/50+ radical 2/50+ radical 3/50+... radical 50/50) is a Riemann sum approximation for

1/50S 1,0 radical x dx

What is the total distance the bug traveled from t=0 to t=8?

13

An equation of the line tangent to the graph of y=2x+3/3x-2 at the point (1,5) is

13x+y=18

The function F is continuous on the closed interval [2,8] and has values that are given in the table above. Using the subintervals [2,5], [5,7], and [7,8], what is the trapezoidal approximation of S 8,2 f(x) dx?

160

What is the instantaneous rate of change at x=2 of the function F given by f(x)=x^2-2/x-1?

2

Let F be a differentiable function such that f(3)=2 and f'(3)=5. If the tangent line to the graph of F at x=3 is used to find an approximation to a zero of F, that approximation is

2.6

The graph of y=3x^4-16x^3+24x^2+48 is concave down for

2/3<x<2

A particle moves along the x-axis so that its position at time T is given by x(t)=t^2-6t+5. For what value of T is the velocity of the particle zero?

3

If f(x)=x^3/2, then f'(4)=

3

The area of the region enclosed by the graph of y=x^2+1 and the line y=5 is

32/3

If the region enclosed by the y-axis, the line y=2, and the curve y= radical x is revolved about the y-axis, the volume of the solid generated is

32pi/5

If f(x)=x radical 2x-3, then f'(x)=

3x-3/radical 2x-3

If f(x)=(x^2-2x-1)^2/3, then f'(0) is

4/3

If the graph of y=ax+b/x+c has a horizontal asymptote y=2 and a vertical asymptote x=-3, then a+c=

5

A bug begins to crawl up a vertical wire at time t=0. The velocity V of the bug at time T, 0_<t_<8, is given by function whose graph is shown above. At what value of T does the bug change direction?

6

S2,1 (4x^3-6x) dx=

6

For what value of X does the function f(x)=(x-2)(x-3)^2 have a relative max?

7/3

If Sb,a f(x)dx=a+2b, then Sb,a (f(x)+5)dx=

7b-4a

If f(x)=tan(2x), then f'(pi/6)=

8

If the base B of a triangle is increasing at a rate of 3 inches per minute while its height H is decreasing at a rate of 3 inches per minute, which of the following must be true about the area A of the triangle?

A is decreasing only when b>h

If F is a differentiable function, then f'(a) is given by which of the following?

I and II only

The function F given by f(x)=x^3=12x-24 is

Increasing for all x

How many critical points does the function f(x)=(x+2)^5(x-3)^4 have?

Nine

d/dx S x,0 cos(2piU) du is

cos(2pix)

S pi/4, 0 e^tanx/cos^2x dx is

e-1

1/2Se^t/2 dt=

e^t/2+C

The graph of the function F is shown above. Which of the following statements about F is true?

lim x>a f(x)=2

If f(x){lnx for 0<x_<2 x^2ln2 for 2<x_<4, then lim x>2 f(x) is

nonexistent

lim x>1 x/lnx is

nonexistent

If f(x)=sin(x/2), then there exists a number C in the interval pi/2<x<3pi/2 that satisfies the conclusion of the Mean Value Theorem. Which of the following could be C?

pi

The average value of cos on the interval [-3,5] is

sin3+sin5/8

The acceleration of a particle moving along the x-axis at time T is given by a(t)=6t-2. If the velocity is 25 when t=3 and the position is 10 when t=1, then the position x(t)=

t^3-t^2+4t+6

An equation of the line tangent to the graph of y=cos(2x) at x=pi/4 is

y=-2(x-pi/4)

An equation of the line tangent to the graph of y=x+cosx at the point (0,1) is

y=x+1

Which of the following is an equation of the line tangent to the graph of f(x)=x^4+2x^2 at the point where f'(x)=1?

y=x-0.122