Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-1+x^4)/(-1+x+x^4-x^3)
- Limit of (2+x^3-3*x)/(-2+x^3-4*x^2+5*x)
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Limit of (-2+x^3)/(-5+9*x)
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Limit of (x+x^3-15*x^2)/(15*x+18*x^2)
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Identical expressions
- a^x- one /x
- a to the power of x minus 1 divide by x
- a to the power of x minus one divide by x
- ax-1/x
- a^x-1 divide by x
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Similar expressions
- a^x+1/x
Limit of the function a^x-1/x
The solution
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/ x 1\ lim |a - -| x->0+\ x/
$$\lim_{x \to 0^+}\left(a^{x} - \frac{1}{x}\right)$$
Limit(a^x - 1/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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(a^{x} - \frac{1}{x}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(a^{x} - \frac{1}{x}\right) = -\infty$$
$$\lim_{x \to \infty}\left(a^{x} - \frac{1}{x}\right)$$
More at x→oo
$$\lim_{x \to 1^-}\left(a^{x} - \frac{1}{x}\right) = a - 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(a^{x} - \frac{1}{x}\right) = a - 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(a^{x} - \frac{1}{x}\right)$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(a^{x} - \frac{1}{x}\right) = -\infty$$
$$\lim_{x \to \infty}\left(a^{x} - \frac{1}{x}\right)$$
More at x→oo
$$\lim_{x \to 1^-}\left(a^{x} - \frac{1}{x}\right) = a - 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(a^{x} - \frac{1}{x}\right) = a - 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(a^{x} - \frac{1}{x}\right)$$
More at x→-oo
One‐sided limits
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/ x 1\ lim |a - -| x->0+\ x/
$$\lim_{x \to 0^+}\left(a^{x} - \frac{1}{x}\right)$$
-oo
$$-\infty$$
/ x 1\ lim |a - -| x->0-\ x/
$$\lim_{x \to 0^-}\left(a^{x} - \frac{1}{x}\right)$$
oo
$$\infty$$
oo