Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1-4*x)^(1/x)
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Limit of (-16+x^2+6*x)/(-2-5*x+3*x^2)
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Limit of (1+x)^(2/3)-(-1+x)^(2/3)
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Limit of 1/3+x/3
- Integral of d{x}:
- x^5*sin(x)
- Derivative of:
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x^5*sin(x)
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Identical expressions
- x^ five *sin(x)
- x to the power of 5 multiply by sinus of (x)
- x to the power of five multiply by sinus of (x)
- x5*sin(x)
- x5*sinx
- x⁵*sin(x)
- x^5sin(x)
- x5sin(x)
- x5sinx
- x^5sinx
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Similar expressions
- x^5*sinx
Limit of the function x^5*sin(x)
The solution
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/ 5 \ lim \x *sin(x)/ x->oo
$$\lim_{x \to \infty}\left(x^{5} \sin{\left(x \right)}\right)$$
Limit(x^5*sin(x), x, oo, dir='-')
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
$$\lim_{x \to \infty}\left(x^{5} \sin{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
$$\lim_{x \to 0^-}\left(x^{5} \sin{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{5} \sin{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{5} \sin{\left(x \right)}\right) = \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{5} \sin{\left(x \right)}\right) = \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{5} \sin{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x^{5} \sin{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{5} \sin{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{5} \sin{\left(x \right)}\right) = \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{5} \sin{\left(x \right)}\right) = \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{5} \sin{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
The graph