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