Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-2+sqrt(x))/(-4+x^2)
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Limit of (-exp(-x)+exp(x))/(exp(x)+exp(-x))
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Limit of x+2*x^3+5*x^4-x^2/3
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Limit of (-x^3+2*x+5*x^4)/(1+x^4-8*x^3)
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Identical expressions
- four *x^ two /(x^ two -x)
- 4 multiply by x squared divide by (x squared minus x)
- four multiply by x to the power of two divide by (x to the power of two minus x)
- 4*x2/(x2-x)
- 4*x2/x2-x
- 4*x²/(x²-x)
- 4*x to the power of 2/(x to the power of 2-x)
- 4x^2/(x^2-x)
- 4x2/(x2-x)
- 4x2/x2-x
- 4x^2/x^2-x
- 4*x^2 divide by (x^2-x)
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Similar expressions
- 4*x^2/(x^2+x)
Limit of the function 4*x^2/(x^2-x)
The solution
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[src]
/ 2 \
| 4*x |
lim |------|
x->0+| 2 |
\x - x/
$$\lim_{x \to 0^+}\left(\frac{4 x^{2}}{x^{2} - x}\right)$$
Limit((4*x^2)/(x^2 - x), x, 0)
Detail solution
Let's take the limit
$$\lim_{x \to 0^+}\left(\frac{4 x^{2}}{x^{2} - x}\right)$$
transform
$$\lim_{x \to 0^+}\left(\frac{4 x^{2}}{x^{2} - x}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{4 x^{2}}{x \left(x - 1\right)}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{4 x}{x - 1}\right) = $$
$$\frac{0 \cdot 4}{-1} = $$
The final answer:
$$\lim_{x \to 0^+}\left(\frac{4 x^{2}}{x^{2} - x}\right) = 0$$
$$\lim_{x \to 0^+}\left(\frac{4 x^{2}}{x^{2} - x}\right)$$
transform
$$\lim_{x \to 0^+}\left(\frac{4 x^{2}}{x^{2} - x}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{4 x^{2}}{x \left(x - 1\right)}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{4 x}{x - 1}\right) = $$
$$\frac{0 \cdot 4}{-1} = $$
= 0
The final answer:
$$\lim_{x \to 0^+}\left(\frac{4 x^{2}}{x^{2} - x}\right) = 0$$
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
$$\lim_{x \to 0^-}\left(\frac{4 x^{2}}{x^{2} - x}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{4 x^{2}}{x^{2} - x}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{4 x^{2}}{x^{2} - x}\right) = 4$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{4 x^{2}}{x^{2} - x}\right) = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{4 x^{2}}{x^{2} - x}\right) = \infty$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{4 x^{2}}{x^{2} - x}\right) = 4$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{4 x^{2}}{x^{2} - x}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{4 x^{2}}{x^{2} - x}\right) = 4$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{4 x^{2}}{x^{2} - x}\right) = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{4 x^{2}}{x^{2} - x}\right) = \infty$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{4 x^{2}}{x^{2} - x}\right) = 4$$
More at x→-oo
One‐sided limits
[src]
/ 2 \
| 4*x |
lim |------|
x->0+| 2 |
\x - x/
$$\lim_{x \to 0^+}\left(\frac{4 x^{2}}{x^{2} - x}\right)$$
0
$$0$$
= -2.38544570312941e-29
/ 2 \
| 4*x |
lim |------|
x->0-| 2 |
\x - x/
$$\lim_{x \to 0^-}\left(\frac{4 x^{2}}{x^{2} - x}\right)$$
0
$$0$$
= 2.93727144208228e-28
= 2.93727144208228e-28
The graph