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anonymous
 one year ago
Find the limit of the function by using direct substitution.
lim> pi/2 (2e^x cosx)
0
1
2e^(pi/2)
pi/2
anonymous
 one year ago
Find the limit of the function by using direct substitution. lim> pi/2 (2e^x cosx) 0 1 2e^(pi/2) pi/2

This Question is Closed

welshfella
 one year ago
Best ResponseYou've already chosen the best response.22 * e^(pi/2) * cos (pi/2) make sure to set your calculator to radians

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle \lim_{x\rightarrow \pi/2}~2e^x\cos(x) =2e^{\pi/2}\cos(\pi/2) }\)

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1What does cos(pi/2) give you?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1That should be a give away

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1This is what direct substitution means here. When you have a limit \(\large\color{black}{ \displaystyle \lim_{x\rightarrow a}~f(x) }\) then, by direct substitution, your limit is equal to \(\large f(a)\).

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(most limits as you have previously seen or going to see, you can't apply direct substitution tho', whether that is fortunate or not....)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(( We can do a taylor approximation here for \(\pi/2\) and for e, if you would like ))

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I will tell you this. If you have: \(\large\color{black}{ \displaystyle \lim_{x\rightarrow a}~f(x) }\) then, for any continous function f(x), direct substitution will work. (unless you have a=±∞)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i got c is that correct? @SolomonZelman @Astrophysics

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1if you don't remember, then, unit circle, or: \(\color{black}{ \displaystyle \cos(90)=\cos(45+45)=\cos(45)\cos(45)\sin(45)\sin(45)=0 }\) (knowing that `sin(45)=cos(45)` => = √2/2)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle \lim_{x\rightarrow \pi/2}~2e^x\cos(x) =2e^{\pi/2}\cdot \cos(\pi/2) =2e^{\pi/2}\cdot 0=?}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, this limit is equivalent to zero.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(yes, 0, from both sides.)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Welcome into the calculus world:) xD Good luck with your math!
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