Mister Exam
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How to use it?
- Limit of the function:
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Limit of ((1+x)/(1+2*x))^x
-
Limit of (n/(1+n))^(5+3*n)
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Limit of (9^x-8^x)/asin(3*x)
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Limit of (-4+2*x+8*x^2)/(6+4*x)
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Identical expressions
- cot(eight *pi*x)
- cotangent of (8 multiply by Pi multiply by x)
- cotangent of (eight multiply by Pi multiply by x)
- cot(8pix)
- cot8pix
Limit of the function cot(8*pi*x)
The solution
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lim cot(8*pi*x) x->2+
$$\lim_{x \to 2^+} \cot{\left(8 \pi x \right)}$$
Limit(cot(8*pi*x), x, 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
One‐sided limits
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lim cot(8*pi*x) x->2+
$$\lim_{x \to 2^+} \cot{\left(8 \pi x \right)}$$
oo
$$\infty$$
= 5.95251570050224
lim cot(8*pi*x) x->2-
$$\lim_{x \to 2^-} \cot{\left(8 \pi x \right)}$$
-oo
$$-\infty$$
= -5.95251570050224
= -5.95251570050224
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 2^-} \cot{\left(8 \pi x \right)} = \infty$$
More at x→2 from the left
$$\lim_{x \to 2^+} \cot{\left(8 \pi x \right)} = \infty$$
$$\lim_{x \to \infty} \cot{\left(8 \pi x \right)} = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-} \cot{\left(8 \pi x \right)} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cot{\left(8 \pi x \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cot{\left(8 \pi x \right)} = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cot{\left(8 \pi x \right)} = \infty$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cot{\left(8 \pi x \right)} = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
More at x→2 from the left
$$\lim_{x \to 2^+} \cot{\left(8 \pi x \right)} = \infty$$
$$\lim_{x \to \infty} \cot{\left(8 \pi x \right)} = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-} \cot{\left(8 \pi x \right)} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cot{\left(8 \pi x \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cot{\left(8 \pi x \right)} = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cot{\left(8 \pi x \right)} = \infty$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cot{\left(8 \pi x \right)} = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
The graph