Question

f(x)=(e^(2+x)^2-e^4)/x find lim (f(x)) as x->0

Answer 1

all over x?

Answer 2

Yes

Answer 3

do you know which indeterminate form this is in?

Answer 4

Do you mean to take ln of top and bottom?

Answer 5

are you familiar with indeterminate forms? this one is easy. what happens when you first substitute 0 in for x in the equation?

Answer 6

I thought your in was ln. Yes I do know the indeterminate forms this 0/0

Answer 7

okay, good. so what happens when we have an indeterminate form. which rule do we apply

Answer 8

Usually with this form we would factor

Answer 9

Or we could use l'hoptials rule

Answer 10

l'hopitals rule seems like a good idea. so what does the expression become when we apply l'hopitals rule

Answer 11

Not sure about numerator denominator would be 1

Answer 12

okay so we need to take the derivative of (e^(2+x)^2-e^4)

let's do it term by term. so find the derivative of -e^4 and e^(2x+x)^2

Answer 13

0

Answer 14

good, and e^(2x+x)^2 ?

Answer 15

(4+2x)e(2+x)^2

Answer 16

oops

Answer 17

i deleted my reply >.< one sec

Answer 18

Thanks for the clues got my answer.

Answer 19

looks good, im going to move things around a bit and make the expression:

lim x -> 0 (2e^(2+x)^2)(2+x)

factoring out the constants we get:

2(lim x->0 e^(2+x)(2+x)

Now the limit of a product is the product of the limits so,

2( lim x -> 0 e^(2+x)) (lim x -> 0 (2+x))

Answer 20

oh okay

Answer 21

nice

Answer 22

i got 4e^4