can someone help me evaluate the limit of this equation limit approaches 0(e^(4x) - 1-4x)/(x^2)

Question

can someone help  me evaluate the limit of this equation limit approaches 0(e^(4x) - 1-4x)/(x^2)

anonymous · Answer

attachment

anonymous · Answer

i get zero over zero

amistre64 · Answer

derive top and bottom seperately; then limit them seperately

amistre64 · Answer

lhopitals rule

amistre64 · Answer

i wonder if you can do that more than once

anonymous · Answer

Yes.  You can do it as long as both the denominator and numerator have 0/0 or ∞/∞

amistre64 · Answer

2x doesnt seem to help does it lol

amistre64 · Answer

you can?  over and over?

anonymous · Answer

yeah as long as you get 0/0 or infin/infin

amistre64 · Answer

i thought i read that somewhere lol

anonymous · Answer

ok so i would get the derivative of the top correct over the derivative of the bottom

amistre64 · Answer

yes

amistre64 · Answer

4.e^4x - 4      2.e^4x - 2
---------- = ---------
     2x                    x

amistre64 · Answer

8.e^4x at 0 = ...8 right?

anonymous · Answer

yeah thats what the answer sheet got  but i still dont understand how you got it

amistre64 · Answer

x^2; 2x ; 2  tese are the derivatives right?  of the bottom

anonymous · Answer

yeah

amistre64 · Answer

e^4x -1 - 4x; 4.e^4x -4; 16.e^4x for the top

amistre64 · Answer

16.e^4x
------- = 8.e^4x ; at x=0; 8.1 = 8
     2

anonymous · Answer

cant see where you get the 16 from sorry

amistre64 · Answer

4.e^4x right?  derive e^4x again and we get:

4. 4.e^4x = 16.e^4x

amistre64 · Answer

e^u derives to :  Du e^u

anonymous · Answer

ok so u used l hopital twice

amistre64 · Answer

yes lol

anonymous · Answer

ok ok awesome and we were just talking about that