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
- x^ two + one /(two *x)
- x squared plus 1 divide by (2 multiply by x)
- x to the power of two plus one divide by (two multiply by x)
- x2+1/(2*x)
- x2+1/2*x
- x²+1/(2*x)
- x to the power of 2+1/(2*x)
- x^2+1/(2x)
- x2+1/(2x)
- x2+1/2x
- x^2+1/2x
- x^2+1 divide by (2*x)
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Similar expressions
- x^2-1/(2*x)
Limit of the function x^2+1/(2*x)
The solution
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[src]
/ 2 1 \ lim |x + ---| x->-1+\ 2*x/
$$\lim_{x \to -1^+}\left(x^{2} + \frac{1}{2 x}\right)$$
Limit(x^2 + 1/(2*x), x, -1)
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
$$\lim_{x \to -1^-}\left(x^{2} + \frac{1}{2 x}\right) = \frac{1}{2}$$
More at x→-1 from the left
$$\lim_{x \to -1^+}\left(x^{2} + \frac{1}{2 x}\right) = \frac{1}{2}$$
$$\lim_{x \to \infty}\left(x^{2} + \frac{1}{2 x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(x^{2} + \frac{1}{2 x}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} + \frac{1}{2 x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} + \frac{1}{2 x}\right) = \frac{3}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} + \frac{1}{2 x}\right) = \frac{3}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} + \frac{1}{2 x}\right) = \infty$$
More at x→-oo
More at x→-1 from the left
$$\lim_{x \to -1^+}\left(x^{2} + \frac{1}{2 x}\right) = \frac{1}{2}$$
$$\lim_{x \to \infty}\left(x^{2} + \frac{1}{2 x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(x^{2} + \frac{1}{2 x}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} + \frac{1}{2 x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} + \frac{1}{2 x}\right) = \frac{3}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} + \frac{1}{2 x}\right) = \frac{3}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} + \frac{1}{2 x}\right) = \infty$$
More at x→-oo
One‐sided limits
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/ 2 1 \ lim |x + ---| x->-1+\ 2*x/
$$\lim_{x \to -1^+}\left(x^{2} + \frac{1}{2 x}\right)$$
1/2
$$\frac{1}{2}$$
= 0.5
/ 2 1 \ lim |x + ---| x->-1-\ 2*x/
$$\lim_{x \to -1^-}\left(x^{2} + \frac{1}{2 x}\right)$$
1/2
$$\frac{1}{2}$$
= 0.5
= 0.5
The graph