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csc(x)
Limit of the function/ csc(x)

Limit of the function csc(x)

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The solution

You have entered [src] 
 lim  csc(x)
x->pi+
lim⁡x→π+csc⁡(x)\lim_{x \to \pi^+} \csc{\left(x \right)} 
Limit(csc(x), x, pi)
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
0123456-6-5-4-3-2-1-50000000000000005000000000000000
Plot the graph
Rapid solution [src] 
-oo
−∞-\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→π−csc⁡(x)=−∞\lim_{x \to \pi^-} \csc{\left(x \right)} = -\infty
More at x→pi from the left
lim⁡x→π+csc⁡(x)=−∞\lim_{x \to \pi^+} \csc{\left(x \right)} = -\infty
lim⁡x→∞csc⁡(x)=⟨−∞,∞⟩\lim_{x \to \infty} \csc{\left(x \right)} = \left\langle -\infty, \infty\right\rangle
More at x→oo
lim⁡x→0−csc⁡(x)=−∞\lim_{x \to 0^-} \csc{\left(x \right)} = -\infty
More at x→0 from the left
lim⁡x→0+csc⁡(x)=∞\lim_{x \to 0^+} \csc{\left(x \right)} = \infty
More at x→0 from the right
lim⁡x→1−csc⁡(x)=1sin⁡(1)\lim_{x \to 1^-} \csc{\left(x \right)} = \frac{1}{\sin{\left(1 \right)}}
More at x→1 from the left
lim⁡x→1+csc⁡(x)=1sin⁡(1)\lim_{x \to 1^+} \csc{\left(x \right)} = \frac{1}{\sin{\left(1 \right)}}
More at x→1 from the right
lim⁡x→−∞csc⁡(x)=⟨−∞,∞⟩\lim_{x \to -\infty} \csc{\left(x \right)} = \left\langle -\infty, \infty\right\rangle
More at x→-oo
One‐sided limits [src] 
 lim  csc(x)
x->pi+
lim⁡x→π+csc⁡(x)\lim_{x \to \pi^+} \csc{\left(x \right)} 
-oo
−∞-\infty 
= -151.00110375841
 lim  csc(x)
x->pi-
lim⁡x→π−csc⁡(x)\lim_{x \to \pi^-} \csc{\left(x \right)} 
oo
∞\infty 
= 151.001103758404
= 151.001103758404
Numerical answer [src] 
-151.00110375841
-151.00110375841
The graph
Limit of the function csc(x)
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