Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-20+x^2-x)/(12+x^2+7*x)
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Limit of (-2+x)/(2+sqrt(x))
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Limit of x^2+1/(2*x)
- Limit of (12+x^2-8*x)/(8+x^2-6*x)
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Identical expressions
- (- two +x)/(two +sqrt(x))
- ( minus 2 plus x) divide by (2 plus square root of (x))
- ( minus two plus x) divide by (two plus square root of (x))
- (-2+x)/(2+√(x))
- -2+x/2+sqrtx
- (-2+x) divide by (2+sqrt(x))
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Similar expressions
- (-2+x)/(2-sqrt(x))
- (2+x)/(2+sqrt(x))
- (-2-x)/(2+sqrt(x))
Limit of the function (-2+x)/(2+sqrt(x))
The solution
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[src]
/ -2 + x \
lim |---------|
x->2+| ___|
\2 + \/ x /
$$\lim_{x \to 2^+}\left(\frac{x - 2}{\sqrt{x} + 2}\right)$$
Limit((-2 + x)/(2 + sqrt(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
$$\lim_{x \to 2^-}\left(\frac{x - 2}{\sqrt{x} + 2}\right) = 0$$
More at x→2 from the left
$$\lim_{x \to 2^+}\left(\frac{x - 2}{\sqrt{x} + 2}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{x - 2}{\sqrt{x} + 2}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x - 2}{\sqrt{x} + 2}\right) = -1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x - 2}{\sqrt{x} + 2}\right) = -1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x - 2}{\sqrt{x} + 2}\right) = - \frac{1}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x - 2}{\sqrt{x} + 2}\right) = - \frac{1}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x - 2}{\sqrt{x} + 2}\right) = \infty i$$
More at x→-oo
More at x→2 from the left
$$\lim_{x \to 2^+}\left(\frac{x - 2}{\sqrt{x} + 2}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{x - 2}{\sqrt{x} + 2}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x - 2}{\sqrt{x} + 2}\right) = -1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x - 2}{\sqrt{x} + 2}\right) = -1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x - 2}{\sqrt{x} + 2}\right) = - \frac{1}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x - 2}{\sqrt{x} + 2}\right) = - \frac{1}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x - 2}{\sqrt{x} + 2}\right) = \infty i$$
More at x→-oo
One‐sided limits
[src]
/ -2 + x \
lim |---------|
x->2+| ___|
\2 + \/ x /
$$\lim_{x \to 2^+}\left(\frac{x - 2}{\sqrt{x} + 2}\right)$$
0
$$0$$
= 1.97610682759051e-32
/ -2 + x \
lim |---------|
x->2-| ___|
\2 + \/ x /
$$\lim_{x \to 2^-}\left(\frac{x - 2}{\sqrt{x} + 2}\right)$$
0
$$0$$
= -1.26331126049591e-33
= -1.26331126049591e-33
The graph