Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-2+x)/(-2+x^2-x)
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Limit of cos(5*x)*sin(2*x)/tan(x)
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Limit of 3*sin(x)^2/(4*x)
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Limit of log(1+e^x)
- Derivative of:
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sin(x)^cos(x)
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Identical expressions
- sin(x)^cos(x)
- sinus of (x) to the power of co sinus of e of (x)
- sin(x)cos(x)
- sinxcosx
- sinx^cosx
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Similar expressions
- sinx^cosx
Limit of the function sin(x)^cos(x)
The solution
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[src]
cos(x) lim sin (x) x->0+
$$\lim_{x \to 0^+} \sin^{\cos{\left(x \right)}}{\left(x \right)}$$
Limit(sin(x)^cos(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
[src]
cos(x) lim sin (x) x->0+
$$\lim_{x \to 0^+} \sin^{\cos{\left(x \right)}}{\left(x \right)}$$
0
$$0$$
= 0.000243262206402705
cos(x) lim sin (x) x->0-
$$\lim_{x \to 0^-} \sin^{\cos{\left(x \right)}}{\left(x \right)}$$
0
$$0$$
= (-1.87404882582739e-11 + 2.92394582441919e-17j)
= (-1.87404882582739e-11 + 2.92394582441919e-17j)
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \sin^{\cos{\left(x \right)}}{\left(x \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sin^{\cos{\left(x \right)}}{\left(x \right)} = 0$$
$$\lim_{x \to \infty} \sin^{\cos{\left(x \right)}}{\left(x \right)} = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-} \sin^{\cos{\left(x \right)}}{\left(x \right)} = \sin^{\cos{\left(1 \right)}}{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sin^{\cos{\left(x \right)}}{\left(x \right)} = \sin^{\cos{\left(1 \right)}}{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sin^{\cos{\left(x \right)}}{\left(x \right)} = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \sin^{\cos{\left(x \right)}}{\left(x \right)} = 0$$
$$\lim_{x \to \infty} \sin^{\cos{\left(x \right)}}{\left(x \right)} = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-} \sin^{\cos{\left(x \right)}}{\left(x \right)} = \sin^{\cos{\left(1 \right)}}{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sin^{\cos{\left(x \right)}}{\left(x \right)} = \sin^{\cos{\left(1 \right)}}{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sin^{\cos{\left(x \right)}}{\left(x \right)} = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
The graph