Mister Exam
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How to use it?
- Limit of the function:
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Limit of (4-x^2)/(3-x^2)
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Limit of (-2+x^2-x)/(-2+x+3*x^2)
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Limit of 5-9*x+3*x^2/2
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Limit of (-16+x^2)/(-64+x^3)
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Identical expressions
- cot(x)^cos(x)
- cotangent of (x) to the power of co sinus of e of (x)
- cot(x)cos(x)
- cotxcosx
- cotx^cosx
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Similar expressions
- cot(x)^cosx
Limit of the function cot(x)^cos(x)
The solution
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cos(x) lim cot (x) pi x->--+ 2
$$\lim_{x \to \frac{\pi}{2}^+} \cot^{\cos{\left(x \right)}}{\left(x \right)}$$
Limit(cot(x)^cos(x), x, pi/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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cos(x) lim cot (x) pi x->--+ 2
$$\lim_{x \to \frac{\pi}{2}^+} \cot^{\cos{\left(x \right)}}{\left(x \right)}$$
1
$$1$$
= (1.00191868618493 - 0.000831463027735788j)
cos(x) lim cot (x) pi x->--- 2
$$\lim_{x \to \frac{\pi}{2}^-} \cot^{\cos{\left(x \right)}}{\left(x \right)}$$
1
$$1$$
= 0.9978981007012
= 0.9978981007012
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \frac{\pi}{2}^-} \cot^{\cos{\left(x \right)}}{\left(x \right)} = 1$$
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+} \cot^{\cos{\left(x \right)}}{\left(x \right)} = 1$$
$$\lim_{x \to \infty} \cot^{\cos{\left(x \right)}}{\left(x \right)}$$
More at x→oo
$$\lim_{x \to 0^-} \cot^{\cos{\left(x \right)}}{\left(x \right)} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cot^{\cos{\left(x \right)}}{\left(x \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cot^{\cos{\left(x \right)}}{\left(x \right)} = \tan^{- \cos{\left(1 \right)}}{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cot^{\cos{\left(x \right)}}{\left(x \right)} = \tan^{- \cos{\left(1 \right)}}{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cot^{\cos{\left(x \right)}}{\left(x \right)}$$
More at x→-oo
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+} \cot^{\cos{\left(x \right)}}{\left(x \right)} = 1$$
$$\lim_{x \to \infty} \cot^{\cos{\left(x \right)}}{\left(x \right)}$$
More at x→oo
$$\lim_{x \to 0^-} \cot^{\cos{\left(x \right)}}{\left(x \right)} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cot^{\cos{\left(x \right)}}{\left(x \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cot^{\cos{\left(x \right)}}{\left(x \right)} = \tan^{- \cos{\left(1 \right)}}{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cot^{\cos{\left(x \right)}}{\left(x \right)} = \tan^{- \cos{\left(1 \right)}}{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cot^{\cos{\left(x \right)}}{\left(x \right)}$$
More at x→-oo
Numerical answer
[src]
(1.00191868618493 - 0.000831463027735788j)
(1.00191868618493 - 0.000831463027735788j)
The graph