Mister Exam
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- Limit of the function:
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Limit of (-5+2*x)^2
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Limit of 4-6*x+2*x^4
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Limit of (2-x)^(3*x/(-1+x))
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Limit of (-3+x-6*x^2+2*x^3)/(-3+x)
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Identical expressions
- cot(x)^tan(x)
- cotangent of (x) to the power of tangent of (x)
- cot(x)tan(x)
- cotxtanx
- cotx^tanx
Limit of the function cot(x)^tan(x)
The solution
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tan(x) lim cot (x) x->0+
$$\lim_{x \to 0^+} \cot^{\tan{\left(x \right)}}{\left(x \right)}$$
Limit(cot(x)^tan(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
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tan(x) lim cot (x) x->0+
$$\lim_{x \to 0^+} \cot^{\tan{\left(x \right)}}{\left(x \right)}$$
1
$$1$$
= 1.00185542670553
tan(x) lim cot (x) x->0-
$$\lim_{x \to 0^-} \cot^{\tan{\left(x \right)}}{\left(x \right)}$$
1
$$1$$
= (0.998093757181672 - 0.000768056678188133j)
= (0.998093757181672 - 0.000768056678188133j)
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \cot^{\tan{\left(x \right)}}{\left(x \right)} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cot^{\tan{\left(x \right)}}{\left(x \right)} = 1$$
$$\lim_{x \to \infty} \cot^{\tan{\left(x \right)}}{\left(x \right)}$$
More at x→oo
$$\lim_{x \to 1^-} \cot^{\tan{\left(x \right)}}{\left(x \right)} = \tan^{- \tan{\left(1 \right)}}{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cot^{\tan{\left(x \right)}}{\left(x \right)} = \tan^{- \tan{\left(1 \right)}}{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cot^{\tan{\left(x \right)}}{\left(x \right)}$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \cot^{\tan{\left(x \right)}}{\left(x \right)} = 1$$
$$\lim_{x \to \infty} \cot^{\tan{\left(x \right)}}{\left(x \right)}$$
More at x→oo
$$\lim_{x \to 1^-} \cot^{\tan{\left(x \right)}}{\left(x \right)} = \tan^{- \tan{\left(1 \right)}}{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cot^{\tan{\left(x \right)}}{\left(x \right)} = \tan^{- \tan{\left(1 \right)}}{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cot^{\tan{\left(x \right)}}{\left(x \right)}$$
More at x→-oo
The graph