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sqrt((1+x)/(1-x))
Limit of the function/ sqrt((1+x)/(1-x))

Limit of the function sqrt((1+x)/(1-x))

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         _______
        / 1 + x 
 lim   /  ----- 
x->0+\/   1 - x
lim⁡x→0+x+11−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
02468-8-6-4-2-101005
Plot the graph
Rapid solution [src] 
1
11
Expand and simplify
One‐sided limits [src] 
         _______
        / 1 + x 
 lim   /  ----- 
x->0+\/   1 - x
lim⁡x→0+x+11−x\lim_{x \to 0^+} \sqrt{\frac{x + 1}{1 - x}} 
1
11 
= 1.0
         _______
        / 1 + x 
 lim   /  ----- 
x->0-\/   1 - x
lim⁡x→0−x+11−x\lim_{x \to 0^-} \sqrt{\frac{x + 1}{1 - x}} 
1
11 
= 1.0
= 1.0
Other limits x→0, -oo, +oo, 1
lim⁡x→0−x+11−x=1\lim_{x \to 0^-} \sqrt{\frac{x + 1}{1 - x}} = 1
More at x→0 from the left
lim⁡x→0+x+11−x=1\lim_{x \to 0^+} \sqrt{\frac{x + 1}{1 - x}} = 1
lim⁡x→∞x+11−x=i\lim_{x \to \infty} \sqrt{\frac{x + 1}{1 - x}} = i
More at x→oo
lim⁡x→1−x+11−x=∞\lim_{x \to 1^-} \sqrt{\frac{x + 1}{1 - x}} = \infty
More at x→1 from the left
lim⁡x→1+x+11−x=∞i\lim_{x \to 1^+} \sqrt{\frac{x + 1}{1 - x}} = \infty i
More at x→1 from the right
lim⁡x→−∞x+11−x=i\lim_{x \to -\infty} \sqrt{\frac{x + 1}{1 - x}} = i
More at x→-oo
Numerical answer [src] 
1.0
1.0
The graph
Limit of the function sqrt((1+x)/(1-x))
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