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cos(x)/x
Limit of the function/ cos(x)/x

Limit of the function cos(x)/x

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     /cos(x)\
 lim |------|
x->0+\  x   /
lim⁡x→0+(cos⁡(x)x)\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)}}{x}\right) 
Limit(cos(x)/x, x, 0)
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
02468-8-6-4-2-1010-200200
Plot the graph
Rapid solution [src] 
oo
∞\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(cos⁡(x)x)=∞\lim_{x \to 0^-}\left(\frac{\cos{\left(x \right)}}{x}\right) = \infty
More at x→0 from the left
lim⁡x→0+(cos⁡(x)x)=∞\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)}}{x}\right) = \infty
lim⁡x→∞(cos⁡(x)x)=0\lim_{x \to \infty}\left(\frac{\cos{\left(x \right)}}{x}\right) = 0
More at x→oo
lim⁡x→1−(cos⁡(x)x)=cos⁡(1)\lim_{x \to 1^-}\left(\frac{\cos{\left(x \right)}}{x}\right) = \cos{\left(1 \right)}
More at x→1 from the left
lim⁡x→1+(cos⁡(x)x)=cos⁡(1)\lim_{x \to 1^+}\left(\frac{\cos{\left(x \right)}}{x}\right) = \cos{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞(cos⁡(x)x)=0\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)}}{x}\right) = 0
More at x→-oo
One‐sided limits [src] 
     /cos(x)\
 lim |------|
x->0+\  x   /
lim⁡x→0+(cos⁡(x)x)\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)}}{x}\right) 
oo
∞\infty 
= 150.996688753824
     /cos(x)\
 lim |------|
x->0-\  x   /
lim⁡x→0−(cos⁡(x)x)\lim_{x \to 0^-}\left(\frac{\cos{\left(x \right)}}{x}\right) 
-oo
−∞-\infty 
= -150.996688753824
= -150.996688753824
Numerical answer [src] 
150.996688753824
150.996688753824
The graph
Limit of the function cos(x)/x
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