Math Is Fun Forum

AbbyMac

Member

Registered: 2010-05-04

Posts: 1

Calculus Homework HELP!!!

Hey everyone! I have a LOT of problems to do by the end of this week and I am stuck on these problems.....if anyone could help me solve these that would be most appreciated. I am just stuck and cannot figure out any of these. I've figured out the other one except these.....

1. Find the indicated limit. Show sandwich inequality.
lim
x→∞ (e-x^3cos x)

2. Solve the problem.
Given f(x) = 8x2, L =200, x0 = 5, and ε = 0.1, find the greatest value for δ > 0 such that 0 < x - x0 < δ ⇒ the
inequality f(x0 - L < ε holds.

3.The driver of a car traveling at 54 ft/sec suddenly applies the brakes. The position of the car is s = 54t - 3t2, t
seconds after the driver applies the brakes. How far does the car go before coming to a stop?

4. Find the second derivative of the function.
r = (1 + 8θ/8θ)(8 - θ)

5.Find dy/dx
e5y = cos (3x +y)

6.Solve the problem.
About how accurately must the interior diameter of a cylindrical storage tank that is 8 m high be measured in
order to calculate the tankʹs volume within 2% of its true value?

7.The strength S of a rectangular wooden beam is proportional to its width times the square of its depth. Find the
dimensions of the strongest beam that can be cut from a 10-in.-diameter cylindrical log. (Round answers to the
nearest thosandth.)

8.Solve the equation using Newtonʹs method.
e-x = 5x - 2 , x0 = 1

9.Find the formula and limit as requested.
For the function f(x) = 9 - 2x2 , find a formula for the right sum obtained by dividing the interval [0, 1] into n
equal subintervals. Then take the limit as n→∞ to calculate the area under the curve over [0,1].

10. Answer the question appropriately?
Find the area of the ʺtriangularʺ region in the first quadrant that is bounded above by the curve y = e3x, below
by the curve y = ex, and on the right by the line x = ln 3.

I got all of the other problems I just need help with these. PLEASE HELP!!! Thanks~~~~Abby <3

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Calculus Homework HELP!!!

Hi AbbyMac;

Welcome to the forum;

For #8 are you sure it isn't e^(-x) ?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Calculus Homework HELP!!!

Let's suppose it is because I really want to do this one. Rework it into this form.

So one root is

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.