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sin(5*x)/x
Limit of the function/ sin(5*x)/x

Limit of the function sin(5*x)/x

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You have entered [src] 
     /sin(5*x)\
 lim |--------|
x->oo\   x    /
lim⁡x→∞(sin⁡(5x)x)\lim_{x \to \infty}\left(\frac{\sin{\left(5 x \right)}}{x}\right) 
Limit(sin(5*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
02468-8-6-4-2-10105-5
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Rapid solution [src] 
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Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(sin⁡(5x)x)=0\lim_{x \to \infty}\left(\frac{\sin{\left(5 x \right)}}{x}\right) = 0
lim⁡x→0−(sin⁡(5x)x)=5\lim_{x \to 0^-}\left(\frac{\sin{\left(5 x \right)}}{x}\right) = 5
More at x→0 from the left
lim⁡x→0+(sin⁡(5x)x)=5\lim_{x \to 0^+}\left(\frac{\sin{\left(5 x \right)}}{x}\right) = 5
More at x→0 from the right
lim⁡x→1−(sin⁡(5x)x)=sin⁡(5)\lim_{x \to 1^-}\left(\frac{\sin{\left(5 x \right)}}{x}\right) = \sin{\left(5 \right)}
More at x→1 from the left
lim⁡x→1+(sin⁡(5x)x)=sin⁡(5)\lim_{x \to 1^+}\left(\frac{\sin{\left(5 x \right)}}{x}\right) = \sin{\left(5 \right)}
More at x→1 from the right
lim⁡x→−∞(sin⁡(5x)x)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(5 x \right)}}{x}\right) = 0
More at x→-oo
The graph
Limit of the function sin(5*x)/x
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