Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 10+x^2+3*x^3+8*x
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Limit of (-2+sqrt(x))/(-4+x^2)
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Limit of x+2*x^3+5*x^4-x^2/3
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Limit of (-x^3+2*x+5*x^4)/(1+x^4-8*x^3)
- Graphing y =:
- cos(x)^cot(2*x)
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Identical expressions
- cos(x)^cot(two *x)
- co sinus of e of (x) to the power of cotangent of (2 multiply by x)
- co sinus of e of (x) to the power of cotangent of (two multiply by x)
- cos(x)cot(2*x)
- cosxcot2*x
- cos(x)^cot(2x)
- cos(x)cot(2x)
- cosxcot2x
- cosx^cot2x
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Similar expressions
- cosx^cot(2*x)
Limit of the function cos(x)^cot(2*x)
The solution
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cot(2*x) lim cos (x) x->0+
$$\lim_{x \to 0^+} \cos^{\cot{\left(2 x \right)}}{\left(x \right)}$$
Limit(cos(x)^cot(2*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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \cos^{\cot{\left(2 x \right)}}{\left(x \right)} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos^{\cot{\left(2 x \right)}}{\left(x \right)} = 1$$
$$\lim_{x \to \infty} \cos^{\cot{\left(2 x \right)}}{\left(x \right)}$$
More at x→oo
$$\lim_{x \to 1^-} \cos^{\cot{\left(2 x \right)}}{\left(x \right)} = \cos^{\frac{1}{\tan{\left(2 \right)}}}{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos^{\cot{\left(2 x \right)}}{\left(x \right)} = \cos^{\frac{1}{\tan{\left(2 \right)}}}{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos^{\cot{\left(2 x \right)}}{\left(x \right)}$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \cos^{\cot{\left(2 x \right)}}{\left(x \right)} = 1$$
$$\lim_{x \to \infty} \cos^{\cot{\left(2 x \right)}}{\left(x \right)}$$
More at x→oo
$$\lim_{x \to 1^-} \cos^{\cot{\left(2 x \right)}}{\left(x \right)} = \cos^{\frac{1}{\tan{\left(2 \right)}}}{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos^{\cot{\left(2 x \right)}}{\left(x \right)} = \cos^{\frac{1}{\tan{\left(2 \right)}}}{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos^{\cot{\left(2 x \right)}}{\left(x \right)}$$
More at x→-oo
One‐sided limits
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cot(2*x) lim cos (x) x->0+
$$\lim_{x \to 0^+} \cos^{\cot{\left(2 x \right)}}{\left(x \right)}$$
1
$$1$$
= 1.0
cot(2*x) lim cos (x) x->0-
$$\lim_{x \to 0^-} \cos^{\cot{\left(2 x \right)}}{\left(x \right)}$$
1
$$1$$
= 1.0
= 1.0
The graph