Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-6+x^2-x)/(6+x^2-5*x)
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Limit of log(1+x^2)/(-e^(-x)+cos(3*x))
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Limit of -2+|-2+x|/x
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Limit of (-4-8*x+8*x^2)/(3+8*x)
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Identical expressions
- - two +|- two +x|/x
- minus 2 plus module of minus 2 plus x| divide by x
- minus two plus module of minus two plus x| divide by x
- -2+|-2+x| divide by x
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Similar expressions
- 2+|-2+x|/x
- -2+|+2+x|/x
- -2+|-2-x|/x
- -2-|-2+x|/x
Limit of the function -2+|-2+x|/x
The solution
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[src]
/ |-2 + x|\ lim |-2 + --------| x->2+\ x /
$$\lim_{x \to 2^+}\left(-2 + \frac{\left|{x - 2}\right|}{x}\right)$$
Limit(-2 + |-2 + x|/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
$$\lim_{x \to 2^-}\left(-2 + \frac{\left|{x - 2}\right|}{x}\right) = -2$$
More at x→2 from the left
$$\lim_{x \to 2^+}\left(-2 + \frac{\left|{x - 2}\right|}{x}\right) = -2$$
$$\lim_{x \to \infty}\left(-2 + \frac{\left|{x - 2}\right|}{x}\right) = -1$$
More at x→oo
$$\lim_{x \to 0^-}\left(-2 + \frac{\left|{x - 2}\right|}{x}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(-2 + \frac{\left|{x - 2}\right|}{x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(-2 + \frac{\left|{x - 2}\right|}{x}\right) = -1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(-2 + \frac{\left|{x - 2}\right|}{x}\right) = -1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(-2 + \frac{\left|{x - 2}\right|}{x}\right) = -3$$
More at x→-oo
More at x→2 from the left
$$\lim_{x \to 2^+}\left(-2 + \frac{\left|{x - 2}\right|}{x}\right) = -2$$
$$\lim_{x \to \infty}\left(-2 + \frac{\left|{x - 2}\right|}{x}\right) = -1$$
More at x→oo
$$\lim_{x \to 0^-}\left(-2 + \frac{\left|{x - 2}\right|}{x}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(-2 + \frac{\left|{x - 2}\right|}{x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(-2 + \frac{\left|{x - 2}\right|}{x}\right) = -1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(-2 + \frac{\left|{x - 2}\right|}{x}\right) = -1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(-2 + \frac{\left|{x - 2}\right|}{x}\right) = -3$$
More at x→-oo
One‐sided limits
[src]
/ |-2 + x|\ lim |-2 + --------| x->2+\ x /
$$\lim_{x \to 2^+}\left(-2 + \frac{\left|{x - 2}\right|}{x}\right)$$
-2
$$-2$$
= -2.0
/ |-2 + x|\ lim |-2 + --------| x->2-\ x /
$$\lim_{x \to 2^-}\left(-2 + \frac{\left|{x - 2}\right|}{x}\right)$$
-2
$$-2$$
= -2.0
= -2.0
The graph