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tan(pi*x/4)
Limit of the function/ tan(pi*x/4)

Limit of the function tan(pi*x/4)

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        /pi*x\
 lim tan|----|
x->1+   \ 4  /
$$\lim_{x \to 1^+} \tan{\left(\frac{\pi x}{4} \right)}$$ 
Limit(tan((pi*x)/4), x, 1)
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
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Rapid solution [src] 
1
$$1$$
Expand and simplify
One‐sided limits [src] 
        /pi*x\
 lim tan|----|
x->1+   \ 4  /
$$\lim_{x \to 1^+} \tan{\left(\frac{\pi x}{4} \right)}$$ 
1
$$1$$ 
= 1.0
        /pi*x\
 lim tan|----|
x->1-   \ 4  /
$$\lim_{x \to 1^-} \tan{\left(\frac{\pi x}{4} \right)}$$ 
1
$$1$$ 
= 1.0
= 1.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 1^-} \tan{\left(\frac{\pi x}{4} \right)} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \tan{\left(\frac{\pi x}{4} \right)} = 1$$
$$\lim_{x \to \infty} \tan{\left(\frac{\pi x}{4} \right)} = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-} \tan{\left(\frac{\pi x}{4} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \tan{\left(\frac{\pi x}{4} \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to -\infty} \tan{\left(\frac{\pi x}{4} \right)} = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
Numerical answer [src] 
1.0
1.0
The graph
Limit of the function tan(pi*x/4)
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