Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of (-6+x^2-x)/(6+x^2-5*x)
-
Limit of log(1+x^2)/(-e^(-x)+cos(3*x))
-
Limit of -2+|-2+x|/x
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Limit of (-4-8*x+8*x^2)/(3+8*x)
- Derivative of:
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8*x
- Integral of d{x}:
- 8*x
- 8*x
-
Identical expressions
- eight *x
- 8 multiply by x
- eight multiply by x
- 8x
Limit of the function 8*x
The solution
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lim (8*x) x->oo
$$\lim_{x \to \infty}\left(8 x\right)$$
Limit(8*x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(8 x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(8 x\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{8} \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{8} \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{8}{u}\right)$$
=
$$\frac{8}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(8 x\right) = \infty$$
$$\lim_{x \to \infty}\left(8 x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(8 x\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{8} \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{8} \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{8}{u}\right)$$
=
$$\frac{8}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(8 x\right) = \infty$$
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
$$\lim_{x \to \infty}\left(8 x\right) = \infty$$
$$\lim_{x \to 0^-}\left(8 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(8 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(8 x\right) = 8$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(8 x\right) = 8$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(8 x\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(8 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(8 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(8 x\right) = 8$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(8 x\right) = 8$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(8 x\right) = -\infty$$
More at x→-oo
The graph