Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((3+x)^2+(3-x)^2)/((3-x)^2-(3+x)^2)
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Limit of (-1+x)/(-2+sqrt(3+x))
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Limit of (-x+tan(x))/x^3
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Limit of (-1+sqrt(x))/(-3+x)
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Identical expressions
- (- one +sqrt(x))/(- three +x)
- ( minus 1 plus square root of (x)) divide by ( minus 3 plus x)
- ( minus one plus square root of (x)) divide by ( minus three plus x)
- (-1+√(x))/(-3+x)
- -1+sqrtx/-3+x
- (-1+sqrt(x)) divide by (-3+x)
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Similar expressions
- (-1+sqrt(x))/(3+x)
- (1+sqrt(x))/(-3+x)
- (-1+sqrt(x))/(-3-x)
- (-1-sqrt(x))/(-3+x)
Limit of the function (-1+sqrt(x))/(-3+x)
The solution
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[src]
/ ___\
|-1 + \/ x |
lim |----------|
x->3+\ -3 + x /
$$\lim_{x \to 3^+}\left(\frac{\sqrt{x} - 1}{x - 3}\right)$$
Limit((-1 + sqrt(x))/(-3 + x), x, 3)
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
$$\lim_{x \to 3^-}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = \infty$$
More at x→3 from the left
$$\lim_{x \to 3^+}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = \frac{1}{3}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = \frac{1}{3}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = 0$$
More at x→-oo
More at x→3 from the left
$$\lim_{x \to 3^+}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = \frac{1}{3}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = \frac{1}{3}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sqrt{x} - 1}{x - 3}\right) = 0$$
More at x→-oo
One‐sided limits
[src]
/ ___\
|-1 + \/ x |
lim |----------|
x->3+\ -3 + x /
$$\lim_{x \to 3^+}\left(\frac{\sqrt{x} - 1}{x - 3}\right)$$
oo
$$\infty$$
= 110.828187940107
/ ___\
|-1 + \/ x |
lim |----------|
x->3-\ -3 + x /
$$\lim_{x \to 3^-}\left(\frac{\sqrt{x} - 1}{x - 3}\right)$$
-oo
$$-\infty$$
= -110.250837319232
= -110.250837319232
The graph