Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (3+2*n)/|-1+2*n|
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Limit of (3+x^2-4*x)/(-9+x^2)
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Limit of (x^2-3*x)/(-8+x^2)
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Limit of (1+5*x)*(-1+5*x)
- Derivative of:
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1-x
- Graphing y =:
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1-x
- Integral of d{x}:
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1-x
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Identical expressions
- one -x
- 1 minus x
- one minus x
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Similar expressions
- 1+x
Limit of the function 1-x
The solution
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lim (1 - x) x->oo
$$\lim_{x \to \infty}\left(1 - x\right)$$
Limit(1 - x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(1 - x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(1 - x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{1}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{1}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{u - 1}{u}\right)$$
=
$$\frac{-1}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(1 - x\right) = -\infty$$
$$\lim_{x \to \infty}\left(1 - x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(1 - x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{1}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{1}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{u - 1}{u}\right)$$
=
$$\frac{-1}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(1 - x\right) = -\infty$$
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
$$\lim_{x \to \infty}\left(1 - x\right) = -\infty$$
$$\lim_{x \to 0^-}\left(1 - x\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(1 - x\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(1 - x\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(1 - x\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(1 - x\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(1 - x\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(1 - x\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(1 - x\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(1 - x\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(1 - x\right) = \infty$$
More at x→-oo
The graph