Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (x^2-x)/(-7+2*x^2+5*x)
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Limit of x^2/(4+x)
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Limit of (-20+x^2-x)/(-4+x^2-3*x)
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Limit of (6+x^2-5*x)/(2-x^2)
- Derivative of:
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sqrt((1+x)/(1-x))
- Graphing y =:
- sqrt((1+x)/(1-x))
- Integral of d{x}:
- sqrt((1+x)/(1-x))
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Identical expressions
- sqrt((one +x)/(one -x))
- square root of ((1 plus x) divide by (1 minus x))
- square root of ((one plus x) divide by (one minus x))
- √((1+x)/(1-x))
- sqrt1+x/1-x
- sqrt((1+x) divide by (1-x))
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Similar expressions
- sqrt((1-x)/(1-x))
- sqrt((1+x)/(1+x))
Limit of the function sqrt((1+x)/(1-x))
The solution
You have entered
[src]
_______
/ 1 + x
lim / -----
x->0+\/ 1 - x
$$\lim_{x \to 0^+} \sqrt{\frac{x + 1}{1 - x}}$$
Limit(sqrt((1 + x)/(1 - 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
One‐sided limits
[src]
_______
/ 1 + x
lim / -----
x->0+\/ 1 - x
$$\lim_{x \to 0^+} \sqrt{\frac{x + 1}{1 - x}}$$
1
$$1$$
= 1.0
_______
/ 1 + x
lim / -----
x->0-\/ 1 - x
$$\lim_{x \to 0^-} \sqrt{\frac{x + 1}{1 - x}}$$
1
$$1$$
= 1.0
= 1.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \sqrt{\frac{x + 1}{1 - x}} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sqrt{\frac{x + 1}{1 - x}} = 1$$
$$\lim_{x \to \infty} \sqrt{\frac{x + 1}{1 - x}} = i$$
More at x→oo
$$\lim_{x \to 1^-} \sqrt{\frac{x + 1}{1 - x}} = \infty$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sqrt{\frac{x + 1}{1 - x}} = \infty i$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sqrt{\frac{x + 1}{1 - x}} = i$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \sqrt{\frac{x + 1}{1 - x}} = 1$$
$$\lim_{x \to \infty} \sqrt{\frac{x + 1}{1 - x}} = i$$
More at x→oo
$$\lim_{x \to 1^-} \sqrt{\frac{x + 1}{1 - x}} = \infty$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sqrt{\frac{x + 1}{1 - x}} = \infty i$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sqrt{\frac{x + 1}{1 - x}} = i$$
More at x→-oo
The graph