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Find the limit of $\tan\left(\frac{\pi x}{4}\right)^{\tan\left(\frac{\pi x}{2}\right)}$ as $x$ approaches $1$

Step-by-step Solution

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Final answer to the problem

$1$
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Step-by-step Solution

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  • Solve using limit properties
  • Solve using direct substitution
  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
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1

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.

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

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Learn how to solve limits of exponential functions problems step by step online. Find the limit of tan((pix)/4)^tan((pix)/2) as x approaches 1. 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.

Final answer to the problem

$1$

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Function Plot

Plotting: $\tan\left(\frac{\pi x}{4}\right)^{\tan\left(\frac{\pi x}{2}\right)}$

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5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

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

How to improve your answer:

Main Topic: Limits of Exponential Functions

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

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