Jusaquikie
  • Jusaquikie
lim 8e^(TanX) x → (π/2)+
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Jusaquikie
  • Jusaquikie
not sure where to go to with this
TuringTest
  • TuringTest
since\[\Large\lim_{x\to a}e^{f(x)}=e^{\lim_{x\to a}f(x)}\]really all you need to know is the limit\[\Large\lim_{x\to\pi/2^+}\tan x\]
TuringTest
  • TuringTest
what is\[\lim_{x\to\pi/2}\tan x\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

TuringTest
  • TuringTest
?
Jusaquikie
  • Jusaquikie
+infinity?
Jusaquikie
  • Jusaquikie
.027
TuringTest
  • TuringTest
actually it depends on the left and right hand approach from the left (x0 from the right (x>pi/2) cos x<0
TuringTest
  • TuringTest
I have no idea where you got that number from....
Jusaquikie
  • Jusaquikie
tan(pi/2) lol
TuringTest
  • TuringTest
I'm gonna take a wild guess and say you left your calculator in degree mode
Jusaquikie
  • Jusaquikie
yes
TuringTest
  • TuringTest
\[\tan x=\frac{\sin x}{\cos x}\]so\[\tan (\pi/2)=\frac{\sin (\pi/2)}{\cos (\pi/2)}=?\]
Jusaquikie
  • Jusaquikie
1/0= undefined
TuringTest
  • TuringTest
right, now what about coming from the right, x>pi/2 will cosince be positive or negative approaching pi/2 from the right?
TuringTest
  • TuringTest
cosine*
Jusaquikie
  • Jusaquikie
positive and increasing to 1?
TuringTest
  • TuringTest
no, what is the cosine of pi/2 ?
Jusaquikie
  • Jusaquikie
0 sorry was thinking sin
Jusaquikie
  • Jusaquikie
so negative
TuringTest
  • TuringTest
correct, so as \(x\to\pi/2^+\) we have that \(\cos x\to0\), which means that\[\lim_{x\to\pi/2^+}\tan x=?\]
Jusaquikie
  • Jusaquikie
0
TuringTest
  • TuringTest
no, think in terms of sin and cos
Jusaquikie
  • Jusaquikie
anything with Euler's number just confuses me, i'm not sure how to treat it
Jusaquikie
  • Jusaquikie
2pi
TuringTest
  • TuringTest
ignore Euler's number, it could be any exponential base, the answer would be the same...\[\lim_{x\to\pi/2^+}\frac{\sin x}{\cos x}=?\]what is sine approaching? what is cos approaching?
TuringTest
  • TuringTest
what is sine approaching? what is cos approaching?
Jusaquikie
  • Jusaquikie
1,0
TuringTest
  • TuringTest
and is that zero being approached from the negative or positive side?
Jusaquikie
  • Jusaquikie
negative?
TuringTest
  • TuringTest
correct, so considering that\[\lim_{x\to\pi/2^+}\tan x=\lim_{x\to\pi/2^+}\frac{\sin x}{\cos x}\to\frac10\]and that that zero is being approached from the negative side, what is the limit?
Jusaquikie
  • Jusaquikie
i can't visualize it and i'm not sure how to graph it in my calculator so i'm trying to relate it to the unit circle
Jusaquikie
  • Jusaquikie
-infinity?
Jusaquikie
  • Jusaquikie
no + infinity
TuringTest
  • TuringTest
|dw:1347837808350:dw|you were right the first time, -infty
TuringTest
  • TuringTest
positive number (sine) being divided by a small negative number (cosine) is a large negative number
TuringTest
  • TuringTest
\[\frac1{-0.1}=-10\]\[\frac1{-0.01}=-100\]\[\frac1{-0.001}=-1000\]etc., so as cos x goes to zero from x>pi/2 we approach \(-\infty\)
TuringTest
  • TuringTest
hence\[\lim_{x\to\pi/2^+}\tan x=-\infty\]
Jusaquikie
  • Jusaquikie
ok
TuringTest
  • TuringTest
so then what is\[\lim_{x\to\pi/2^+}8e^{\tan x}\]
Jusaquikie
  • Jusaquikie
zero?
TuringTest
  • TuringTest
correct :)
Jusaquikie
  • Jusaquikie
thanks for the long journey, i'm just really tired and burnt out right now, sorry you had to work so hard on this one
TuringTest
  • TuringTest
it's fine, much better than just pumping out an answer you won't comprehend hopefully you learned something is the idea ;)
Jusaquikie
  • Jusaquikie
yes thanks

Looking for something else?

Not the answer you are looking for? Search for more explanations.