Use L'Hopital's Rule to calculate:
lim e^3t -1
------- (e-1, e is raised to 3t)
t
t -0

Question

Use L'Hopital's Rule to calculate:
lim     e^3t -1
         -------   (e-1, e is raised to 3t)
               t
t ->0

amistre64 · Answer

whats that stuff in (..)

anonymous · Answer

just explaining what the numerator is, in case anyone was confused.

amistre64 · Answer

ok, and the other question i have is; if there is no x to limit in this, where do plug in the values for x at?>

anonymous · Answer

opps its suppose to be as x goes to 0, not t. sorry

amistre64 · Answer

ok, x to 0

the value of t as x goes to 0 is t

the value of e^-3t -1 as x goes to 0 is e^-3t-1

amistre64 · Answer

same concept but with the e^3t lol

amistre64 · Answer

Lhop is used for indeterminant conditions, such as 0/0 and inf/inf

amistre64 · Answer

lol, i see you change x to t now

anonymous · Answer

yea lol it was suppose to be t not x.

amistre64 · Answer

ok, so lets take the derivative of the top and the derivative of the bottm; and ratio them so see how fast they are moving during any given point

amistre64 · Answer

derivate of t wrt t is?

anonymous · Answer

what is "wrt"?

amistre64 · Answer

its the lazy form of "With Respect To"

anonymous · Answer

ooo ok lol. so t would be 0 or 1. i think it's 0 tho.

amistre64 · Answer

$$\frac{d}{dt}t\to\frac{dt}{dt}=1$$

amistre64 · Answer

now for the harder one :)

what is e^3t -1 wrt t?

anonymous · Answer

lol. 3e^2t??

amistre64 · Answer

very close; except for bases the exponent stays put.
$$D[x^n]=nx^{n-1}$$
$$D[B^{nx}]=nB^{nx}+ln(B)$$

amistre64 · Answer

not + but *

amistre64 · Answer

so$$D[e^3{t}]\to3e^{3t}ln(e)=3e^{3t}$$

amistre64 · Answer

if i could work the latex code correctly that would be more impressive; as is you kinda gotta use your imagination :)

anonymous · Answer

lol. that was easier than i thought! thanks for doing it step by step with me. :)

amistre64 · Answer

so the limit of 3e^(3t) as t moves to 0 is:  3

amistre64 · Answer

yw