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

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

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      /   tan(x)  \
 lim  |-----------|
   pi \log(cos(x))/
x->--+             
   2
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\tan{\left(x \right)}}{\log{\left(\cos{\left(x \right)} \right)}}\right)$$ 
Limit(tan(x)/log(cos(x)), x, pi/2)
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] 
oo
$$\infty$$
Expand and simplify
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \frac{\pi}{2}^-}\left(\frac{\tan{\left(x \right)}}{\log{\left(\cos{\left(x \right)} \right)}}\right) = \infty$$
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\tan{\left(x \right)}}{\log{\left(\cos{\left(x \right)} \right)}}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\tan{\left(x \right)}}{\log{\left(\cos{\left(x \right)} \right)}}\right)$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\tan{\left(x \right)}}{\log{\left(\cos{\left(x \right)} \right)}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\tan{\left(x \right)}}{\log{\left(\cos{\left(x \right)} \right)}}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\tan{\left(x \right)}}{\log{\left(\cos{\left(x \right)} \right)}}\right) = \frac{\tan{\left(1 \right)}}{\log{\left(\cos{\left(1 \right)} \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\tan{\left(x \right)}}{\log{\left(\cos{\left(x \right)} \right)}}\right) = \frac{\tan{\left(1 \right)}}{\log{\left(\cos{\left(1 \right)} \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\tan{\left(x \right)}}{\log{\left(\cos{\left(x \right)} \right)}}\right)$$
More at x→-oo
One‐sided limits [src] 
      /   tan(x)  \
 lim  |-----------|
   pi \log(cos(x))/
x->--+             
   2
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\tan{\left(x \right)}}{\log{\left(\cos{\left(x \right)} \right)}}\right)$$ 
oo
$$\infty$$ 
= (21.6192721506854 + 13.5369861405391j)
      /   tan(x)  \
 lim  |-----------|
   pi \log(cos(x))/
x->---             
   2
$$\lim_{x \to \frac{\pi}{2}^-}\left(\frac{\tan{\left(x \right)}}{\log{\left(\cos{\left(x \right)} \right)}}\right)$$ 
-oo
$$-\infty$$ 
= -30.0955054157044
= -30.0955054157044
Numerical answer [src] 
(21.6192721506854 + 13.5369861405391j)
(21.6192721506854 + 13.5369861405391j)
The graph
Limit of the function tan(x)/log(cos(x))
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