Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-2+sqrt(x))/(-4+x^2)
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Limit of (-exp(-x)+exp(x))/(exp(x)+exp(-x))
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Limit of x+2*x^3+5*x^4-x^2/3
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Limit of (-x^3+2*x+5*x^4)/(1+x^4-8*x^3)
- Integral of d{x}:
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e^(x/3)
- Derivative of:
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e^(x/3)
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Identical expressions
- e^(x/ three)
- e to the power of (x divide by 3)
- e to the power of (x divide by three)
- e(x/3)
- ex/3
- e^x/3
- e^(x divide by 3)
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Similar expressions
- (x+e^x)/(3*x)
Limit of the function e^(x/3)
The solution
You have entered
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x
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3
lim E
x->oo
$$\lim_{x \to \infty} e^{\frac{x}{3}}$$
Limit(E^(x/3), 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
$$\lim_{x \to \infty} e^{\frac{x}{3}} = \infty$$
$$\lim_{x \to 0^-} e^{\frac{x}{3}} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} e^{\frac{x}{3}} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} e^{\frac{x}{3}} = e^{\frac{1}{3}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} e^{\frac{x}{3}} = e^{\frac{1}{3}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} e^{\frac{x}{3}} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} e^{\frac{x}{3}} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} e^{\frac{x}{3}} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} e^{\frac{x}{3}} = e^{\frac{1}{3}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} e^{\frac{x}{3}} = e^{\frac{1}{3}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} e^{\frac{x}{3}} = 0$$
More at x→-oo
The graph