Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-3+3*x^2)/(-3+sqrt(8+x))
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Limit of (-24*x+3*x^2)/(-64+x^2)
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Limit of (-4+3*x^2+11*x)/(-8+x^2+2*x)
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Limit of ((1+3*x)/(2+3*x))^(-1+2*x)
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Identical expressions
- sqrt(one - two *x)
- square root of (1 minus 2 multiply by x)
- square root of (one minus two multiply by x)
- √(1-2*x)
- sqrt(1-2x)
- sqrt1-2x
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Similar expressions
- sqrt(1-2*x+3*x^2)-(1+x)/x^(1/3)
- sqrt(1+2*x)
Limit of the function sqrt(1-2*x)
The solution
You have entered
[src]
_________ lim \/ 1 - 2*x x->0+
$$\lim_{x \to 0^+} \sqrt{1 - 2 x}$$
Limit(sqrt(1 - 2*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
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \sqrt{1 - 2 x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sqrt{1 - 2 x} = 1$$
$$\lim_{x \to \infty} \sqrt{1 - 2 x} = \infty i$$
More at x→oo
$$\lim_{x \to 1^-} \sqrt{1 - 2 x} = i$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sqrt{1 - 2 x} = i$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sqrt{1 - 2 x} = \infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \sqrt{1 - 2 x} = 1$$
$$\lim_{x \to \infty} \sqrt{1 - 2 x} = \infty i$$
More at x→oo
$$\lim_{x \to 1^-} \sqrt{1 - 2 x} = i$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sqrt{1 - 2 x} = i$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sqrt{1 - 2 x} = \infty$$
More at x→-oo
One‐sided limits
[src]
_________ lim \/ 1 - 2*x x->0+
$$\lim_{x \to 0^+} \sqrt{1 - 2 x}$$
1
$$1$$
= 1.0
_________ lim \/ 1 - 2*x x->0-
$$\lim_{x \to 0^-} \sqrt{1 - 2 x}$$
1
$$1$$
= 1.0
= 1.0
The graph