Mister Exam

Other calculators:

(x/2)^tan(x)
Limit of the function/ (x/2)^tan(x)

Limit of the function (x/2)^tan(x)

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
        tan(x)
     /x\      
 lim |-|      
x->0+\2/
$$\lim_{x \to 0^+} \left(\frac{x}{2}\right)^{\tan{\left(x \right)}}$$ 
Limit((x/2)^tan(x), x, 0)
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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \left(\frac{x}{2}\right)^{\tan{\left(x \right)}} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{x}{2}\right)^{\tan{\left(x \right)}} = 1$$
$$\lim_{x \to \infty} \left(\frac{x}{2}\right)^{\tan{\left(x \right)}}$$
More at x→oo
$$\lim_{x \to 1^-} \left(\frac{x}{2}\right)^{\tan{\left(x \right)}} = 2^{- \tan{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{x}{2}\right)^{\tan{\left(x \right)}} = 2^{- \tan{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{x}{2}\right)^{\tan{\left(x \right)}}$$
More at x→-oo
Rapid solution [src] 
1
$$1$$
Expand and simplify
One‐sided limits [src] 
        tan(x)
     /x\      
 lim |-|      
x->0+\2/
$$\lim_{x \to 0^+} \left(\frac{x}{2}\right)^{\tan{\left(x \right)}}$$ 
1
$$1$$ 
= 0.997980164315909
        tan(x)
     /x\      
 lim |-|      
x->0-\2/
$$\lim_{x \to 0^-} \left(\frac{x}{2}\right)^{\tan{\left(x \right)}}$$ 
1
$$1$$ 
= (1.0021052001677 - 0.000828548038935303j)
= (1.0021052001677 - 0.000828548038935303j)
Numerical answer [src] 
0.997980164315909
0.997980164315909
The graph
Limit of the function (x/2)^tan(x)
    © Mister Exam – Calculator