Find the limit of $\cos\left(\frac{1}{x}\right)^2$ as $x$ approaches $\infty $

Step-by-step Solution

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Final answer to the problem

$1$
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Step-by-step Solution

How should I solve this problem?

  • Solve using direct substitution
  • Solve using L'Hôpital's rule
  • Solve without using l'Hôpital
  • Solve using limit properties
  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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1

Apply the power rule for limits: $\lim_{x\to a}\left(f(x)\right)^n=\left(\lim_{x\to a}f(x)\right)^n$

${\left(\lim_{x\to\infty }\left(\cos\left(\frac{1}{x}\right)\right)\right)}^2$

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${\left(\lim_{x\to\infty }\left(\cos\left(\frac{1}{x}\right)\right)\right)}^2$

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Learn how to solve problems step by step online. Find the limit of cos(1/x)^2 as x approaches infinity. Apply the power rule for limits: \lim_{x\to a}\left(f(x)\right)^n=\left(\lim_{x\to a}f(x)\right)^n. Because cosine is a continuous function, we can bring the limit inside of the cosine. Evaluate the limit \lim_{x\to\infty }\left(\frac{1}{x}\right) by replacing all occurrences of x by \infty . The cosine of 0 equals 1.

Final answer to the problem

$1$

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Function Plot

Plotting: $\cos\left(\frac{1}{x}\right)^2$

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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

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