Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((2+x)/(4+x))^cos(x)
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Limit of -5-2*x^2+8*x
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Limit of (-9+x^2)/(-27+x^3)
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Limit of 1+7*x+11*x^2/2
- Graphing y =:
- x/(1+x)
- Integral of d{x}:
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x/(1+x)
- Derivative of:
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x/(1+x)
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Identical expressions
- x/(one +x)
- x divide by (1 plus x)
- x divide by (one plus x)
- x/1+x
- x divide by (1+x)
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Similar expressions
- (3+x^2+2*x)/(1+x^2)
- 4*x/(1+x^2)
- exp(x)/(1+x)
- x/(1-x)
- (3+x^2+4*x)/(1+x^3)
Limit of the function x/(1+x)
The solution
You have entered
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/ x \ lim |-----| x->1+\1 + x/
$$\lim_{x \to 1^+}\left(\frac{x}{x + 1}\right)$$
Limit(x/(1 + 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
$$\lim_{x \to 1^-}\left(\frac{x}{x + 1}\right) = \frac{1}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{x + 1}\right) = \frac{1}{2}$$
$$\lim_{x \to \infty}\left(\frac{x}{x + 1}\right) = 1$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x}{x + 1}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x}{x + 1}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to -\infty}\left(\frac{x}{x + 1}\right) = 1$$
More at x→-oo
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{x + 1}\right) = \frac{1}{2}$$
$$\lim_{x \to \infty}\left(\frac{x}{x + 1}\right) = 1$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x}{x + 1}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x}{x + 1}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to -\infty}\left(\frac{x}{x + 1}\right) = 1$$
More at x→-oo
One‐sided limits
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/ x \ lim |-----| x->1+\1 + x/
$$\lim_{x \to 1^+}\left(\frac{x}{x + 1}\right)$$
1/2
$$\frac{1}{2}$$
= 0.5
/ x \ lim |-----| x->1-\1 + x/
$$\lim_{x \to 1^-}\left(\frac{x}{x + 1}\right)$$
1/2
$$\frac{1}{2}$$
= 0.5
= 0.5
The graph