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

Step-by-step Solution

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asinh
acosh
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Final answer to the problem

$1$
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Step-by-step Solution

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  • Solve using L'Hôpital's rule
  • Solve without using l'Hôpital
  • 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
  • FOIL Method
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1

Simplifying

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

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

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

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Learn how to solve limits of exponential functions problems step by step online. Find the limit of x^tan(pi*1/2x) as x approaches 1. Simplifying. Evaluate the limit \lim_{x\to1}\left(x^{\tan\left(\frac{\pi}{2}x\right)}\right) by replacing all occurrences of x by 1. Multiply \frac{\pi}{2} times 1. Calculating the tangent of \frac{\pi}{2} degrees.

Final answer to the problem

$1$

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Function Plot

Plotting: $x^{\tan\left(\pi \cdot \frac{1}{2}x\right)}$

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Answer Assistant

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Got a different answer? Verify it!

Go!
1
2
3
4
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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