Mister Exam

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Limit of the function:
Limit of (e^x-e^2)/(-2+x)
Limit of (-asin(x)+2*x)/(2*x+atan(x))
Limit of 2^(-n)*2^(1+n)
Limit of (-6+x^2-x)/(9+x^2-6*x)
Identical expressions
log(x)*tan(x)/cos(two *x)
logarithm of (x) multiply by tangent of (x) divide by co sinus of e of (2 multiply by x)
logarithm of (x) multiply by tangent of (x) divide by co sinus of e of (two multiply by x)
log(x)tan(x)/cos(2x)
logxtanx/cos2x
log(x)*tan(x) divide by cos(2*x)

Limit of the function log(x)tan(x)/cos(2x)

You have entered [src]

      /log(x)*tan(x)\
 lim  |-------------|
   pi \   cos(2*x)  /
x->--+               
   4

\lim_{x \to \frac{\pi}{4}^+}\left(\frac{\log{\left(x \right)} \tan{\left(x \right)}}{\cos{\left(2 x \right)}}\right)

Limit((log(x)*tan(x))/cos(2*x), x, pi/4)

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

One‐sided limits [src]

      /log(x)*tan(x)\
 lim  |-------------|
   pi \   cos(2*x)  /
x->--+               
   4

\lim_{x \to \frac{\pi}{4}^+}\left(\frac{\log{\left(x \right)} \tan{\left(x \right)}}{\cos{\left(2 x \right)}}\right)

oo

\infty

= 17.8394143979694

      /log(x)*tan(x)\
 lim  |-------------|
   pi \   cos(2*x)  /
x->---               
   4

\lim_{x \to \frac{\pi}{4}^-}\left(\frac{\log{\left(x \right)} \tan{\left(x \right)}}{\cos{\left(2 x \right)}}\right)

-oo

-\infty

= -18.6295906058945

= -18.6295906058945

Other limits x→0, -oo, +oo, 1

\lim_{x \to \frac{\pi}{4}^-}\left(\frac{\log{\left(x \right)} \tan{\left(x \right)}}{\cos{\left(2 x \right)}}\right) = \infty

\lim_{x \to \frac{\pi}{4}^+}\left(\frac{\log{\left(x \right)} \tan{\left(x \right)}}{\cos{\left(2 x \right)}}\right) = \infty

\lim_{x \to \infty}\left(\frac{\log{\left(x \right)} \tan{\left(x \right)}}{\cos{\left(2 x \right)}}\right)

\lim_{x \to 0^-}\left(\frac{\log{\left(x \right)} \tan{\left(x \right)}}{\cos{\left(2 x \right)}}\right) = 0

\lim_{x \to 0^+}\left(\frac{\log{\left(x \right)} \tan{\left(x \right)}}{\cos{\left(2 x \right)}}\right) = 0

\lim_{x \to 1^-}\left(\frac{\log{\left(x \right)} \tan{\left(x \right)}}{\cos{\left(2 x \right)}}\right) = 0

\lim_{x \to 1^+}\left(\frac{\log{\left(x \right)} \tan{\left(x \right)}}{\cos{\left(2 x \right)}}\right) = 0

\lim_{x \to -\infty}\left(\frac{\log{\left(x \right)} \tan{\left(x \right)}}{\cos{\left(2 x \right)}}\right)

Numerical answer [src]

17.8394143979694

17.8394143979694

The graph

Limit of the function log(x)*tan(x)/cos(2*x)