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:
#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.
Hello, c_323_h!
Cody (Galactus) is right . . . there is a slick way.
You may already know it, though.
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.