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

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

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     /cos(x) + sin(x)\
 lim |---------------|
x->oo\       x       /
lim⁡x→∞(sin⁡(x)+cos⁡(x)x)\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right) 
Limit((cos(x) + sin(x))/x, x, oo, dir='-')
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
02468-8-6-4-2-1010-2020
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Rapid solution [src] 
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Other limits x→0, -oo, +oo, 1
lim⁡x→∞(sin⁡(x)+cos⁡(x)x)=0\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right) = 0
lim⁡x→0−(sin⁡(x)+cos⁡(x)x)=−∞\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right) = -\infty
More at x→0 from the left
lim⁡x→0+(sin⁡(x)+cos⁡(x)x)=∞\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right) = \infty
More at x→0 from the right
lim⁡x→1−(sin⁡(x)+cos⁡(x)x)=cos⁡(1)+sin⁡(1)\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right) = \cos{\left(1 \right)} + \sin{\left(1 \right)}
More at x→1 from the left
lim⁡x→1+(sin⁡(x)+cos⁡(x)x)=cos⁡(1)+sin⁡(1)\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right) = \cos{\left(1 \right)} + \sin{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞(sin⁡(x)+cos⁡(x)x)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right) = 0
More at x→-oo
The graph
Limit of the function (cos(x)+sin(x))/x
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