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Limit of the function tan(x/2)

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         /x\
 lim  tan|-|
   pi    \2/
x->--+      
   2

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

Limit(tan(x/2), 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]

1

Expand and simplify

One‐sided limits [src]

         /x\
 lim  tan|-|
   pi    \2/
x->--+      
   2

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

1

= 1.0

         /x\
 lim  tan|-|
   pi    \2/
x->---      
   2

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

1

= 1.0

= 1.0

Other limits x→0, -oo, +oo, 1

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

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

\lim_{x \to \infty} \tan{\left(\frac{x}{2} \right)} = \left\langle -\infty, \infty\right\rangle

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

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

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

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

\lim_{x \to -\infty} \tan{\left(\frac{x}{2} \right)} = \left\langle -\infty, \infty\right\rangle

Numerical answer [src]

1.0

1.0

The graph