Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of sin(3)^3/x^2
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Limit of log(sin(x)/x)
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Limit of log(log(x))/x
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Limit of 2*sin(2*x)
- Sum of series:
- x*a^x
- Derivative of:
- x*a^x
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Identical expressions
- x*a^x
- x multiply by a to the power of x
- x*ax
- xa^x
- xax
Limit of the function x*a^x
The solution
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/ x\ lim \x*a / x->oo
$$\lim_{x \to \infty}\left(a^{x} x\right)$$
Limit(x*a^x, x, oo, dir='-')
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(a^{x} x\right)$$
$$\lim_{x \to 0^-}\left(a^{x} x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(a^{x} x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(a^{x} x\right) = a$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(a^{x} x\right) = a$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(a^{x} x\right)$$
More at x→-oo
$$\lim_{x \to 0^-}\left(a^{x} x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(a^{x} x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(a^{x} x\right) = a$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(a^{x} x\right) = a$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(a^{x} x\right)$$
More at x→-oo