Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (1+3*x)^(5/x)
-
Limit of (-16+x^2+6*x)/(-2-5*x+3*x^2)
-
Limit of (1+x)^(2/3)-(-1+x)^(2/3)
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Limit of e^(1+3*x)*(-1+x)
- Graphing y =:
- -4*x
- Integral of d{x}:
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-4*x
- Derivative of:
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-4*x
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Identical expressions
- - four *x
- minus 4 multiply by x
- minus four multiply by x
- -4x
-
Similar expressions
- 4*x
Limit of the function -4*x
The solution
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lim (-4*x) x->oo
$$\lim_{x \to \infty}\left(- 4 x\right)$$
Limit(-4*x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(- 4 x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(- 4 x\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{4} \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{4} \frac{1}{x}} = \lim_{u \to 0^+}\left(- \frac{4}{u}\right)$$
=
$$- \frac{4}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(- 4 x\right) = -\infty$$
$$\lim_{x \to \infty}\left(- 4 x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(- 4 x\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{4} \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{4} \frac{1}{x}} = \lim_{u \to 0^+}\left(- \frac{4}{u}\right)$$
=
$$- \frac{4}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(- 4 x\right) = -\infty$$
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
$$\lim_{x \to \infty}\left(- 4 x\right) = -\infty$$
$$\lim_{x \to 0^-}\left(- 4 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- 4 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- 4 x\right) = -4$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- 4 x\right) = -4$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- 4 x\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(- 4 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- 4 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- 4 x\right) = -4$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- 4 x\right) = -4$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- 4 x\right) = \infty$$
More at x→-oo
The graph