anonymous
  • anonymous
Use L'Hopital's Rule to calculate: lim e^3t -1 ------- (e-1, e is raised to 3t) t t ->0
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
amistre64
  • amistre64
whats that stuff in (..)
anonymous
  • anonymous
just explaining what the numerator is, in case anyone was confused.
amistre64
  • amistre64
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?>

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anonymous
  • anonymous
opps its suppose to be as x goes to 0, not t. sorry
amistre64
  • amistre64
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
  • amistre64
same concept but with the e^3t lol
amistre64
  • amistre64
Lhop is used for indeterminant conditions, such as 0/0 and inf/inf
amistre64
  • amistre64
lol, i see you change x to t now
anonymous
  • anonymous
yea lol it was suppose to be t not x.
amistre64
  • amistre64
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
  • amistre64
derivate of t wrt t is?
anonymous
  • anonymous
what is "wrt"?
amistre64
  • amistre64
its the lazy form of "With Respect To"
anonymous
  • anonymous
ooo ok lol. so t would be 0 or 1. i think it's 0 tho.
amistre64
  • amistre64
\[\frac{d}{dt}t\to\frac{dt}{dt}=1\]
amistre64
  • amistre64
now for the harder one :) what is e^3t -1 wrt t?
anonymous
  • anonymous
lol. 3e^2t??
amistre64
  • amistre64
very close; except for bases the exponent stays put. \[D[x^n]=nx^{n-1}\] \[D[B^{nx}]=nB^{nx}+ln(B)\]
amistre64
  • amistre64
not + but *
amistre64
  • amistre64
so\[D[e^3{t}]\to3e^{3t}ln(e)=3e^{3t}\]
amistre64
  • amistre64
if i could work the latex code correctly that would be more impressive; as is you kinda gotta use your imagination :)
anonymous
  • anonymous
lol. that was easier than i thought! thanks for doing it step by step with me. :)
amistre64
  • amistre64
so the limit of 3e^(3t) as t moves to 0 is: 3
amistre64
  • amistre64
yw

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