Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 7*tan(9*x/5)/x
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Limit of (2+x^2-3*x)/(3+x^2-4*x)
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Limit of -2+e^x-e^(-x)-sin(x)
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Limit of (2-7*x+3*x^2)/(2-5*x+2*x^2)
- Sum of series:
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1/3
- Derivative of:
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1/3
- Integral of d{x}:
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1/3
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Identical expressions
- one / three
- 1 divide by 3
- one divide by three
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Similar expressions
- (1-1/(3*x))^(6*x)
- -1/(3*x^3)
Limit of the function 1/3
The solution
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
$$\lim_{x \to 0^-} \frac{1}{3} = \frac{1}{3}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{3} = \frac{1}{3}$$
$$\lim_{x \to \infty} \frac{1}{3} = \frac{1}{3}$$
More at x→oo
$$\lim_{x \to 1^-} \frac{1}{3} = \frac{1}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{3} = \frac{1}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{3} = \frac{1}{3}$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{3} = \frac{1}{3}$$
$$\lim_{x \to \infty} \frac{1}{3} = \frac{1}{3}$$
More at x→oo
$$\lim_{x \to 1^-} \frac{1}{3} = \frac{1}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{3} = \frac{1}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{3} = \frac{1}{3}$$
More at x→-oo
One‐sided limits
[src]
lim (1/3) x->0+
$$\lim_{x \to 0^+} \frac{1}{3}$$
1/3
$$\frac{1}{3}$$
= 0.333333333333333
lim (1/3) x->0-
$$\lim_{x \to 0^-} \frac{1}{3}$$
1/3
$$\frac{1}{3}$$
= 0.333333333333333
= 0.333333333333333