# A few Short Calculus Practice Problems- HELP!

• Dec 11th 2008, 01:35 PM
Sm10389
A few Short Calculus Practice Problems- HELP!
Can anyone please show me how to do these? I'm in short calculus (calc without trig).

If $

\int_1^4 f(x)dx = 6
$
, what is the value of the integral $

\int_1^4 f(5-x)dx$
?
A. 6 B. -6 C. 3 D. 0

If $y^2 - 2xy=16$ then $\frac{dy}{dx}=$
a. $\frac{x}{y-x}$ b. $\frac{2y}{y-x}$ c. $\frac{y}{x-y}$ d. $\frac{y}{y-x}$

The area enclosed by $x(1-x)$ and the x axis is
a. 1/6 b. 1 c. 5/6 d/ 2/3

A particle travels in a straight line with a constant acceleration of 3 $\frac{m}{s^2}$. 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

Let $f(x)=ln\sqrt{x^2+1}$ then f'(1)=
a. 1/3 b. 1/2 c. 3/2 d. 2/3

At what value does the function $f(x)= x^3*e^{-x}$ obtain its maximum value?
a. 3 b. 0 c.e d. √3

Compute $\int_1^4 \sqrt{t}ln t dt$
4ln4_____4/3 ln4______16/3*ln4-28/9______22/3*ln4-25/9

If y is defined at $\frac{dy}{dx}+xy=x$ and y(0)=0, then y(1)=
1-e___1-1/√e_____1-√e_______2-1/√e

On which of the following intervals does $x^5*3x^2+pi=0$ have a solution?
[1,2] [0,1] [-1,0] [-2,-1]

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

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

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

Solve the following differential equations:
$\frac{dy}{dx}= \frac{1}{x+1}$ where y(0)=1
$\frac{dy}{dt}=y^2*xe^{-x}$

Integral from +inf to 1 of 1/√x dx

Calculate the following integrals:
$\int \frac{ln{x}}{x^{2}}{dx} =
$

$

\int \frac{1}{\sqrt{x}}$
from 1 to +infinity =
[/tex]

Thanks for any help!
• Dec 11th 2008, 02:34 PM
skeeter
For a "short" calculus course, this list of laundry covers a wide swath of concepts.

I can provide some hints, but I don't think you'll get anyone to show you how to do all these "few" problems in detail. Good luck.

Quote:

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

• Dec 11th 2008, 02:55 PM
Sm10389
Thank you.
I still have a few questions (for starters):

#1.) I know substitution but don't know how to use it here.
#2.) Didn't work out correctly.
#3.) Figured it out, but don't know how you found the interval [0,1]
#4.) Don't understand at all.
• Dec 11th 2008, 03:16 PM
Sm10389
More questions:
#5: I got -1/2, which is not an option, correct answer is 3/2 but idk how.
#6: Don't know how to find critical points with e's.
#7: Used integration by parts, answer wasn't on here.
#8: Wouldn't it be x(-1-y)?
#9: Solved, thanks.
#10: Still don't understand.
#11: For the derivative I got 1-(1/x) what is the slope of that?
#12: Still don't understand.
#13: Still don't understand.
#14: Solved, thanks.
#15: Solved, thanks.
#16: How would I know that by looking at it?

Thanks.