Originally Posted by

**Sm10389** Can anyone please show me how to do these? I'm in short calculus (calc without trig).

If the integral of f(x)dx=6 from 1 to 4, what is the value of the integral f(5-x)dx from 1 to 4?

a. 6 b. -6 c. 3 d. 0

use substitution ... let u = 5-x

If y^2 - 2xy=16 then dy/dx=

a. x/(y-x) b. 2y/(y-x) c. y/(x-y) d. y/(y-x)

implicit differentiation ... do it.

The area enclosed by x(1-x) and the x axis is

a. 1/6 b. 1 c. 5/6 d/ 2/3

A = definite integral of x(1-x) from 0 to 1

A particle travels in a straight line with a constant acceleration of 3 m/s^2. if the velocity of the particle is 10 m/s at time 2s, how far does the particle travel during the time interval when its velocity increases from 4 m/s to 10 m/s

a. 20 b. 14 c. 7 d.6

integrate a = 3 and use the initial condition to find v(t) ... displacement will be the integral of v(t) from 0 to 2 sec

Let f(x)=ln(√(x^2+1)) then f'(1)=

a. 1/3 b. 1/2 c. 3/2 d. 2/3

ln(√(x^2+1)) = (1/2)ln(x^2+1) ... derivative of ln(u) = u'/u

At what value does the function f(x)= x^3e^-x obtain its maximum value

a. 3 b. 0 c.e d. √3

max will occur where f'(x) changes sign from positive to negative

Compute the integral of √t*lnt dt on the interval 1 to 4.

4ln4 4/3 ln4 16/3ln4-28/9 22/3ln4-25/9

integration by parts ... u = ln(t) , dv = √t dt

If y is defined at dy/dx+xy=x and y(0)=0, then y(1)=

1-e 1-1/√e 1-√e 2-1/√e

dy/dx = x(1-y) ... separate variables and integrate.

On which of the following intervals does x^5-3x^2+pi=0 have a solution

[1,2] [0,1] [-1,0] [-2,-1]

use the **Intermediate Value Theorem**

Using the definition of the derivative and the fact that d/dx*a^x = a^x*ln a, what is the value of the limit of (a^h -1)/h as h approaches 0

ln a 1 DNE a^h*ln a

f(x) = a^x ... f'(0) = [f(0+h) - f(0)]/h

Determine the equation of the tangent line to y=x-lnx at x=e

x = e , y = e-1 ... find the slope, y'(e), then use the point-slope form for a linear equation.

For the equation F(v)= Av^2 + (B/v^2) where a and b are constants, the drag is minimized when v=5. Find the ratio of B/A

F'(5) = 0 and F''(5) > 0

Solve the following differential equations:

dy/dx= 1/(x+1) where y(0)=1

this one is very basic ... you do it.

dy/dt=y^2*xe^-x

I think you mean dy/dx ... separate variables and integrate.

Calculate the following integrals:

Integral of ln(x)/x^2 dx

integration by parts ... u = ln(x) , dv = 1/x^2

Integral from +inf to 1 of 1/√x dx

you should already know that this integral diverges