Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-5+7*n)/(2+n)
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Limit of (-2+x)/(-4+x)
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Limit of (-16+x^2-6*x)/(-2+x+x^2)
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Limit of (2+x^2-5*x)/(5+x^2+3*x^3)
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Identical expressions
- sqrt(four - two *x)
- square root of (4 minus 2 multiply by x)
- square root of (four minus two multiply by x)
- √(4-2*x)
- sqrt(4-2x)
- sqrt4-2x
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Similar expressions
- sqrt(x+5*x^2)-sqrt(4-2*x+5*x^2)
- sqrt(4+2*x)
Limit of the function sqrt(4-2*x)
The solution
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[src]
_________ lim \/ 4 - 2*x x->2+
$$\lim_{x \to 2^+} \sqrt{4 - 2 x}$$
Limit(sqrt(4 - 2*x), x, 2)
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
$$\lim_{x \to 2^-} \sqrt{4 - 2 x} = 0$$
More at x→2 from the left
$$\lim_{x \to 2^+} \sqrt{4 - 2 x} = 0$$
$$\lim_{x \to \infty} \sqrt{4 - 2 x} = \infty i$$
More at x→oo
$$\lim_{x \to 0^-} \sqrt{4 - 2 x} = 2$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sqrt{4 - 2 x} = 2$$
More at x→0 from the right
$$\lim_{x \to 1^-} \sqrt{4 - 2 x} = \sqrt{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sqrt{4 - 2 x} = \sqrt{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sqrt{4 - 2 x} = \infty$$
More at x→-oo
More at x→2 from the left
$$\lim_{x \to 2^+} \sqrt{4 - 2 x} = 0$$
$$\lim_{x \to \infty} \sqrt{4 - 2 x} = \infty i$$
More at x→oo
$$\lim_{x \to 0^-} \sqrt{4 - 2 x} = 2$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sqrt{4 - 2 x} = 2$$
More at x→0 from the right
$$\lim_{x \to 1^-} \sqrt{4 - 2 x} = \sqrt{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sqrt{4 - 2 x} = \sqrt{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sqrt{4 - 2 x} = \infty$$
More at x→-oo
One‐sided limits
[src]
_________ lim \/ 4 - 2*x x->2+
$$\lim_{x \to 2^+} \sqrt{4 - 2 x}$$
0
$$0$$
= (0.0 + 0.0199956290562172j)
_________ lim \/ 4 - 2*x x->2-
$$\lim_{x \to 2^-} \sqrt{4 - 2 x}$$
0
$$0$$
= 0.0198820998757912
= 0.0198820998757912
The graph