Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (1+3*x)^(5/x)
-
Limit of x^2/(-2+sqrt(4+x^2))
-
Limit of ((5+x^2-6*x)/(5+x^2-5*x))^(2+3*x)
-
Limit of (2+x^2+3*x)/(-4+x^2)
- Derivative of:
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1/(1-x)
- Graphing y =:
- 1/(1-x)
- Integral of d{x}:
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1/(1-x)
-
Identical expressions
- one /(one -x)
- 1 divide by (1 minus x)
- one divide by (one minus x)
- 1/1-x
- 1 divide by (1-x)
-
Similar expressions
- acot(1/(1-x^2))
- 1/(1+e^(1/(1-x^2)))
- x^(1/(1-x^2))
- 1/(1+x)
Limit of the function 1/(1-x)
The solution
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1 lim ----- x->oo1 - x
$$\lim_{x \to \infty} \frac{1}{1 - x}$$
Limit(1/(1 - x), x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty} \frac{1}{1 - x}$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty} \frac{1}{1 - x}$$ =
$$\lim_{x \to \infty}\left(\frac{1}{x \left(-1 + \frac{1}{x}\right)}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1}{x \left(-1 + \frac{1}{x}\right)}\right) = \lim_{u \to 0^+}\left(\frac{u}{u - 1}\right)$$
=
$$\frac{0}{-1} = 0$$
The final answer:
$$\lim_{x \to \infty} \frac{1}{1 - x} = 0$$
$$\lim_{x \to \infty} \frac{1}{1 - x}$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty} \frac{1}{1 - x}$$ =
$$\lim_{x \to \infty}\left(\frac{1}{x \left(-1 + \frac{1}{x}\right)}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1}{x \left(-1 + \frac{1}{x}\right)}\right) = \lim_{u \to 0^+}\left(\frac{u}{u - 1}\right)$$
=
$$\frac{0}{-1} = 0$$
The final answer:
$$\lim_{x \to \infty} \frac{1}{1 - x} = 0$$
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
$$\lim_{x \to \infty} \frac{1}{1 - x} = 0$$
$$\lim_{x \to 0^-} \frac{1}{1 - x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{1 - x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{1 - x} = \infty$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{1 - x} = -\infty$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{1 - x} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \frac{1}{1 - x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{1 - x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{1 - x} = \infty$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{1 - x} = -\infty$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{1 - x} = 0$$
More at x→-oo
The graph