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sin(8*x)/tan(4*x)
Limit of the function/ sin(8*x)/tan(4*x)

Limit of the function sin(8*x)/tan(4*x)

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     /sin(8*x)\
 lim |--------|
x->oo\tan(4*x)/
$$\lim_{x \to \infty}\left(\frac{\sin{\left(8 x \right)}}{\tan{\left(4 x \right)}}\right)$$ 
Limit(sin(8*x)/tan(4*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
Plot the graph
Rapid solution [src] 
     /sin(8*x)\
 lim |--------|
x->oo\tan(4*x)/
$$\lim_{x \to \infty}\left(\frac{\sin{\left(8 x \right)}}{\tan{\left(4 x \right)}}\right)$$
Expand and simplify
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\frac{\sin{\left(8 x \right)}}{\tan{\left(4 x \right)}}\right)$$
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(8 x \right)}}{\tan{\left(4 x \right)}}\right) = 2$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(8 x \right)}}{\tan{\left(4 x \right)}}\right) = 2$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(8 x \right)}}{\tan{\left(4 x \right)}}\right) = \frac{\sin{\left(8 \right)}}{\tan{\left(4 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(8 x \right)}}{\tan{\left(4 x \right)}}\right) = \frac{\sin{\left(8 \right)}}{\tan{\left(4 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(8 x \right)}}{\tan{\left(4 x \right)}}\right)$$
More at x→-oo
The graph
Limit of the function sin(8*x)/tan(4*x)
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