Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (3-3*x^2+4*x^4+6*x^3)/(2*x^2+7*x^4)
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Limit of ((5+4*x)/(-1+5*x))^(1+3*x)
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Limit of (1+x^3-2*x)/(8+x^10-9*x)
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Limit of -2+x^2/3
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Identical expressions
- sqrt(- four + six *x)/(- two +sqrt(x))
- square root of ( minus 4 plus 6 multiply by x) divide by ( minus 2 plus square root of (x))
- square root of ( minus four plus six multiply by x) divide by ( minus two plus square root of (x))
- √(-4+6*x)/(-2+√(x))
- sqrt(-4+6x)/(-2+sqrt(x))
- sqrt-4+6x/-2+sqrtx
- sqrt(-4+6*x) divide by (-2+sqrt(x))
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Similar expressions
- sqrt(-4-6*x)/(-2+sqrt(x))
- sqrt(-4+6*x)/(-2-sqrt(x))
- sqrt(4+6*x)/(-2+sqrt(x))
- sqrt(-4+6*x)/(2+sqrt(x))
Limit of the function sqrt(-4+6*x)/(-2+sqrt(x))
The solution
You have entered
[src]
/ __________\
|\/ -4 + 6*x |
lim |------------|
x->4+| ___ |
\ -2 + \/ x /
$$\lim_{x \to 4^+}\left(\frac{\sqrt{6 x - 4}}{\sqrt{x} - 2}\right)$$
Limit(sqrt(-4 + 6*x)/(-2 + sqrt(x)), x, 4)
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
$$\lim_{x \to 4^-}\left(\frac{\sqrt{6 x - 4}}{\sqrt{x} - 2}\right) = \infty$$
More at x→4 from the left
$$\lim_{x \to 4^+}\left(\frac{\sqrt{6 x - 4}}{\sqrt{x} - 2}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\sqrt{6 x - 4}}{\sqrt{x} - 2}\right) = \sqrt{6}$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\sqrt{6 x - 4}}{\sqrt{x} - 2}\right) = - i$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sqrt{6 x - 4}}{\sqrt{x} - 2}\right) = - i$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sqrt{6 x - 4}}{\sqrt{x} - 2}\right) = - \sqrt{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sqrt{6 x - 4}}{\sqrt{x} - 2}\right) = - \sqrt{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sqrt{6 x - 4}}{\sqrt{x} - 2}\right) = \sqrt{6}$$
More at x→-oo
More at x→4 from the left
$$\lim_{x \to 4^+}\left(\frac{\sqrt{6 x - 4}}{\sqrt{x} - 2}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\sqrt{6 x - 4}}{\sqrt{x} - 2}\right) = \sqrt{6}$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\sqrt{6 x - 4}}{\sqrt{x} - 2}\right) = - i$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sqrt{6 x - 4}}{\sqrt{x} - 2}\right) = - i$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sqrt{6 x - 4}}{\sqrt{x} - 2}\right) = - \sqrt{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sqrt{6 x - 4}}{\sqrt{x} - 2}\right) = - \sqrt{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sqrt{6 x - 4}}{\sqrt{x} - 2}\right) = \sqrt{6}$$
More at x→-oo
The graph