Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 2+((-1+x)/(3+x))^x
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Limit of (-1+x)/(x+x^2)
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Limit of ((1+x)^4-(-1+x)^4)/((1+x)^4+(-1+x)^4)
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Limit of tan(6*x)/(3*x)
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Identical expressions
- (- one +x)/(x+x^ two)
- ( minus 1 plus x) divide by (x plus x squared )
- ( minus one plus x) divide by (x plus x to the power of two)
- (-1+x)/(x+x2)
- -1+x/x+x2
- (-1+x)/(x+x²)
- (-1+x)/(x+x to the power of 2)
- -1+x/x+x^2
- (-1+x) divide by (x+x^2)
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Similar expressions
- (1+x)/(x+x^2)
- (-1+x)/(x-x^2)
- (-1-x)/(x+x^2)
Limit of the function (-1+x)/(x+x^2)
The solution
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[src]
/-1 + x\
lim |------|
x->1+| 2|
\x + x /
$$\lim_{x \to 1^+}\left(\frac{x - 1}{x^{2} + x}\right)$$
Limit((-1 + x)/(x + x^2), x, 1)
Detail solution
Let's take the limit
$$\lim_{x \to 1^+}\left(\frac{x - 1}{x^{2} + x}\right)$$
transform
$$\lim_{x \to 1^+}\left(\frac{x - 1}{x^{2} + x}\right)$$
=
$$\lim_{x \to 1^+}\left(\frac{x - 1}{x \left(x + 1\right)}\right)$$
=
$$\lim_{x \to 1^+}\left(\frac{x - 1}{x \left(x + 1\right)}\right) = $$
$$\frac{-1 + 1}{1 + 1} = $$
The final answer:
$$\lim_{x \to 1^+}\left(\frac{x - 1}{x^{2} + x}\right) = 0$$
$$\lim_{x \to 1^+}\left(\frac{x - 1}{x^{2} + x}\right)$$
transform
$$\lim_{x \to 1^+}\left(\frac{x - 1}{x^{2} + x}\right)$$
=
$$\lim_{x \to 1^+}\left(\frac{x - 1}{x \left(x + 1\right)}\right)$$
=
$$\lim_{x \to 1^+}\left(\frac{x - 1}{x \left(x + 1\right)}\right) = $$
$$\frac{-1 + 1}{1 + 1} = $$
= 0
The final answer:
$$\lim_{x \to 1^+}\left(\frac{x - 1}{x^{2} + x}\right) = 0$$
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
$$\lim_{x \to 1^-}\left(\frac{x - 1}{x^{2} + x}\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x - 1}{x^{2} + x}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{x - 1}{x^{2} + x}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x - 1}{x^{2} + x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x - 1}{x^{2} + x}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to -\infty}\left(\frac{x - 1}{x^{2} + x}\right) = 0$$
More at x→-oo
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x - 1}{x^{2} + x}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{x - 1}{x^{2} + x}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x - 1}{x^{2} + x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x - 1}{x^{2} + x}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to -\infty}\left(\frac{x - 1}{x^{2} + x}\right) = 0$$
More at x→-oo
One‐sided limits
[src]
/-1 + x\
lim |------|
x->1+| 2|
\x + x /
$$\lim_{x \to 1^+}\left(\frac{x - 1}{x^{2} + x}\right)$$
0
$$0$$
= 7.27864599832406e-29
/-1 + x\
lim |------|
x->1-| 2|
\x + x /
$$\lim_{x \to 1^-}\left(\frac{x - 1}{x^{2} + x}\right)$$
0
$$0$$
= 6.05462511935933e-36
= 6.05462511935933e-36
The graph