Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (5+x-3*x^2)/(4-x+2*x^2)
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Limit of (4-x^2)/(3-x^2)
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Limit of (3+2*x)/(1-5*x)
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Limit of (1-2*cos(x))/sin(3*x)
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Identical expressions
- a^x/x
- a to the power of x divide by x
- ax/x
- a^x divide by x
Limit of the function a^x/x
The solution
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/ x\
|a |
lim |--|
x->oo\x /
$$\lim_{x \to \infty}\left(\frac{a^{x}}{x}\right)$$
Limit(a^x/x, x, oo, dir='-')
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\frac{a^{x}}{x}\right)$$
$$\lim_{x \to 0^-}\left(\frac{a^{x}}{x}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{a^{x}}{x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{a^{x}}{x}\right) = a$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{a^{x}}{x}\right) = a$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{a^{x}}{x}\right)$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{a^{x}}{x}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{a^{x}}{x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{a^{x}}{x}\right) = a$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{a^{x}}{x}\right) = a$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{a^{x}}{x}\right)$$
More at x→-oo