Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((2+x)/(4+x))^cos(x)
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Limit of -5-2*x^2+8*x
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Limit of (-9+x^2)/(-27+x^3)
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Limit of 1+7*x+11*x^2/2
- Derivative of:
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-1/3
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Identical expressions
- - one / three
- minus 1 divide by 3
- minus one divide by three
- -1 divide by 3
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Similar expressions
- -1/(3+x)+6/(9-x^2)
- 1/3
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
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 2^-} - \frac{1}{3} = - \frac{1}{3}$$
More at x→2 from the left
$$\lim_{x \to 2^+} - \frac{1}{3} = - \frac{1}{3}$$
$$\lim_{x \to \infty} - \frac{1}{3} = - \frac{1}{3}$$
More at x→oo
$$\lim_{x \to 0^-} - \frac{1}{3} = - \frac{1}{3}$$
More at x→0 from the left
$$\lim_{x \to 0^+} - \frac{1}{3} = - \frac{1}{3}$$
More at x→0 from the right
$$\lim_{x \to 1^-} - \frac{1}{3} = - \frac{1}{3}$$
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→2 from the left
$$\lim_{x \to 2^+} - \frac{1}{3} = - \frac{1}{3}$$
$$\lim_{x \to \infty} - \frac{1}{3} = - \frac{1}{3}$$
More at x→oo
$$\lim_{x \to 0^-} - \frac{1}{3} = - \frac{1}{3}$$
More at x→0 from the left
$$\lim_{x \to 0^+} - \frac{1}{3} = - \frac{1}{3}$$
More at x→0 from the right
$$\lim_{x \to 1^-} - \frac{1}{3} = - \frac{1}{3}$$
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->2+
$$\lim_{x \to 2^+} - \frac{1}{3}$$
-1/3
$$- \frac{1}{3}$$
= -0.333333333333333
lim (-1/3) x->2-
$$\lim_{x \to 2^-} - \frac{1}{3}$$
-1/3
$$- \frac{1}{3}$$
= -0.333333333333333
= -0.333333333333333
The graph