Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-2*x^2+4*x^3+5*x)/(3*x^2+7*x)
-
Limit of (-cos(5*x)+cos(3*x))/x^2
-
Limit of (-1+cos(7*x))/(-1+cos(3*x))
-
Limit of (16+x^2+10*x)/(-6+x^2-x)
- Graphing y =:
-
x/(1-x)
- Derivative of:
-
x/(1-x)
- Integral of d{x}:
-
x/(1-x)
-
Identical expressions
- x/(one -x)
- x divide by (1 minus x)
- x divide by (one minus x)
- x/1-x
- x divide by (1-x)
-
Similar expressions
- 2*x/(1-x^2)
- x*cosh(1/x)/(1-x^2)
- x/(1+x)
- (1+x)/(1-x)
- ((1+x)/(2+x))^((1-sqrt(x))/(1-x))
- pi^2*sin(x)/(1-x^2)
Limit of the function x/(1-x)
The solution
You have entered
[src]
/ x \ lim |-----| x->1+\1 - x/
$$\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right)$$
Limit(x/(1 - x), x, 1)
Detail solution
Let's take the limit
$$\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right)$$
transform
$$\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right)$$
=
$$\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right)$$
=
$$\lim_{x \to 1^+}\left(- \frac{x}{x - 1}\right) = $$
$$\left(-1\right) 1 \cdot \frac{1}{-1 + 1} = $$
The final answer:
$$\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right) = -\infty$$
$$\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right)$$
transform
$$\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right)$$
=
$$\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right)$$
=
$$\lim_{x \to 1^+}\left(- \frac{x}{x - 1}\right) = $$
$$\left(-1\right) 1 \cdot \frac{1}{-1 + 1} = $$
= -oo
The final answer:
$$\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right) = -\infty$$
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
$$\lim_{x \to 1^-}\left(\frac{x}{- x + 1}\right) = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{x}{- x + 1}\right) = -1$$
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
$$\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{x}{- x + 1}\right) = -1$$
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
[src]
/ x \ lim |-----| x->1+\1 - x/
$$\lim_{x \to 1^+}\left(\frac{x}{- x + 1}\right)$$
-oo
$$-\infty$$
= -152.0
/ x \ lim |-----| x->1-\1 - x/
$$\lim_{x \to 1^-}\left(\frac{x}{- x + 1}\right)$$
oo
$$\infty$$
= 150.0
= 150.0
The graph