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# Find the limit $\lim_{x\to1}\left(\tan\left(\frac{\pi x}{4}\right)^{\tan\left(\frac{\pi x}{2}\right)}\right)$

## Step-by-step Solution

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##  Step-by-step Solution 

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Take $\frac{\pi }{4}$ out of the fraction

$\lim_{x\to1}\left(\tan\left(\frac{\pi}{4}x\right)^{\tan\left(\frac{\pi x}{2}\right)}\right)$

Learn how to solve limits of exponential functions problems step by step online.

$\lim_{x\to1}\left(\tan\left(\frac{\pi}{4}x\right)^{\tan\left(\frac{\pi x}{2}\right)}\right)$

Learn how to solve limits of exponential functions problems step by step online. Find the limit (x)->(1)lim(tan((pix)/4)^tan((pix)/2)). Take \frac{\pi }{4} out of the fraction. Take \frac{\pi }{2} out of the fraction. Evaluate the limit \lim_{x\to1}\left(\tan\left(\frac{\pi}{4}x\right)^{\tan\left(\frac{\pi}{2}x\right)}\right) by replacing all occurrences of x by 1. Multiply \frac{\pi}{4} times 1.

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##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Limits by Direct SubstitutionLimits by L'Hôpital's ruleLimits by factoringLimits by rationalizing

SnapXam A2

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a
b
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m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
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e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Main Topic: Limits of Exponential Functions

Those are limits of expressions of the form f(x)^g(x).