Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 1-x-sin(x/2)/pi
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Limit of (1-cos(x)^2)/x
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Limit of (1-cos(4*x))/(4*x^2)
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Limit of (1+8*x)^(1/x)
- Graphing y =:
- (1+sin(x))^cot(x)
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Identical expressions
- (one +sin(x))^cot(x)
- (1 plus sinus of (x)) to the power of cotangent of (x)
- (one plus sinus of (x)) to the power of cotangent of (x)
- (1+sin(x))cot(x)
- 1+sinxcotx
- 1+sinx^cotx
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Similar expressions
- (1-sin(x))^cot(x)
- (1+sinx)^cot(x)
Limit of the function (1+sin(x))^cot(x)
The solution
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cot(x) lim (1 + sin(x)) x->1+
$$\lim_{x \to 1^+} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}}$$
Limit((1 + sin(x))^cot(x), x, 1)
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
Rapid solution
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1
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tan(1)
(1 + sin(1))
$$\left(\sin{\left(1 \right)} + 1\right)^{\frac{1}{\tan{\left(1 \right)}}}$$
One‐sided limits
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cot(x) lim (1 + sin(x)) x->1+
$$\lim_{x \to 1^+} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}}$$
1
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tan(1)
(1 + sin(1))
$$\left(\sin{\left(1 \right)} + 1\right)^{\frac{1}{\tan{\left(1 \right)}}}$$
= 1.47999555699277
cot(x) lim (1 + sin(x)) x->1-
$$\lim_{x \to 1^-} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}}$$
1
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tan(1)
(1 + sin(1))
$$\left(\sin{\left(1 \right)} + 1\right)^{\frac{1}{\tan{\left(1 \right)}}}$$
= 1.47999555699277
= 1.47999555699277
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 1^-} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}} = \left(\sin{\left(1 \right)} + 1\right)^{\frac{1}{\tan{\left(1 \right)}}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}} = \left(\sin{\left(1 \right)} + 1\right)^{\frac{1}{\tan{\left(1 \right)}}}$$
$$\lim_{x \to \infty} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}}$$
More at x→oo
$$\lim_{x \to 0^-} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}} = e$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}} = e$$
More at x→0 from the right
$$\lim_{x \to -\infty} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}}$$
More at x→-oo
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}} = \left(\sin{\left(1 \right)} + 1\right)^{\frac{1}{\tan{\left(1 \right)}}}$$
$$\lim_{x \to \infty} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}}$$
More at x→oo
$$\lim_{x \to 0^-} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}} = e$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}} = e$$
More at x→0 from the right
$$\lim_{x \to -\infty} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}}$$
More at x→-oo
The graph