Mister Exam

# Limit of the function cot(pi*x)*sin(x)/(2*sec(x))

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### The solution

You have entered [src]
     /cot(pi*x)*sin(x)\
lim |----------------|
x->0+\    2*sec(x)    /
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right)$$
Limit((cot(pi*x)*sin(x))/((2*sec(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
One‐sided limits [src]
     /cot(pi*x)*sin(x)\
lim |----------------|
x->0+\    2*sec(x)    /
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right)$$
 1
----
2*pi
$$\frac{1}{2 \pi}$$
= 0.159154943091895
     /cot(pi*x)*sin(x)\
lim |----------------|
x->0-\    2*sec(x)    /
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right)$$
 1
----
2*pi
$$\frac{1}{2 \pi}$$
= 0.159154943091895
= 0.159154943091895
Rapid solution [src]
 1
----
2*pi
$$\frac{1}{2 \pi}$$
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right) = \frac{1}{2 \pi}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right) = \frac{1}{2 \pi}$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right)$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right) = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right) = \infty$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right)$$
More at x→-oo
0.159154943091895
0.159154943091895