Hi guys I have a test tomorrow and am confused on a few homework questions on L'Hospital's Rule and partial fractions

1. Using L'Hospital's Rule:

2. L'Hospital's Rule:

3. Partial Fractions:

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- Jul 25th 2006, 01:44 PMc_323_hNeed help on L'Hospitals, Partial fractions
Hi guys I have a test tomorrow and am confused on a few homework questions on L'Hospital's Rule and partial fractions

1. Using L'Hospital's Rule:

2. L'Hospital's Rule:

3. Partial Fractions:

- Jul 25th 2006, 04:04 PMgalactus
#1.

Do L'hopital twice.

That is, take the derivative of the numerator and denominators twice

The second derivative of is 2.

You have:

Now, as x approaches 0, you have**1/2**

For #2. I believe you may have a 'tan' in your future.

For #3.

Equate coefficients:

Solve the system.

Soroban has a slick way of doing partial fractions. I trust he'll be along to demonstrate. - Jul 25th 2006, 07:57 PMSoroban
Hello, c_323_h!

Cody (Galactus) is right . . . there is a slick way.

You may already know it, though.

Quote:

3. Partial Fractions: .

We have the set up: .

Multiply through by the LCD:

. .

Now pick some "good" values for*****

Let

Let

Let

Therefore: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

*****I hope it's obvious that "good" values are

. . those that create*zeros*in the expression.

- Jul 25th 2006, 08:35 PMc_323_hQuote:

Originally Posted by**Soroban**

thanks to galactus too - Jul 25th 2006, 08:39 PMThePerfectHackerQuote:

Originally Posted by**c_323_h**

Derivative of numerator,

Derivative of denominator,

Thus,

---

I recommend to avoid L'Hopital but rather do,

as