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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3*x
- Integral of d{x}:
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3*x
- Graphing y =:
- 3*x
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Identical expressions
- three *x
- 3 multiply by x
- three multiply by x
- 3x
Limit of the function 3*x
The solution
Detail solution
Let's take the limit
$$\lim_{x \to -\infty}\left(3 x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to -\infty}\left(3 x\right)$$ =
$$\lim_{x \to -\infty} \frac{1}{\frac{1}{3} \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to -\infty} \frac{1}{\frac{1}{3} \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{3}{u}\right)$$
=
$$\frac{3}{0} = -\infty$$
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:
$$\lim_{x \to -\infty}\left(3 x\right)$$ =
$$\lim_{x \to -\infty} \frac{1}{\frac{1}{3} \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to -\infty} \frac{1}{\frac{1}{3} \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{3}{u}\right)$$
=
$$\frac{3}{0} = -\infty$$
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
$$\lim_{x \to -\infty}\left(3 x\right) = -\infty$$
$$\lim_{x \to \infty}\left(3 x\right) = \infty$$
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
$$\lim_{x \to 0^-}\left(3 x\right) = 0$$
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
The graph