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