Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of 10+x^2+3*x^3+8*x
-
Limit of (-2+sqrt(x))/(-4+x^2)
-
Limit of x+2*x^3+5*x^4-x^2/3
-
Limit of (-x^3+2*x+5*x^4)/(1+x^4-8*x^3)
- Graphing y =:
- 3-3*x
-
Identical expressions
- three - three *x
- 3 minus 3 multiply by x
- three minus three multiply by x
- 3-3x
-
Similar expressions
- (x^3-3^x)/(-3+x)
- 3+3*x
Limit of the function 3-3*x
The solution
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lim (3 - 3*x) x->oo
$$\lim_{x \to \infty}\left(3 - 3 x\right)$$
Limit(3 - 3*x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(3 - 3 x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(3 - 3 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{-3 + \frac{3}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{-3 + \frac{3}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{3 u - 3}{u}\right)$$
=
$$\frac{-3 + 0 \cdot 3}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(3 - 3 x\right) = -\infty$$
$$\lim_{x \to \infty}\left(3 - 3 x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(3 - 3 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{-3 + \frac{3}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{-3 + \frac{3}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{3 u - 3}{u}\right)$$
=
$$\frac{-3 + 0 \cdot 3}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(3 - 3 x\right) = -\infty$$
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
$$\lim_{x \to \infty}\left(3 - 3 x\right) = -\infty$$
$$\lim_{x \to 0^-}\left(3 - 3 x\right) = 3$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(3 - 3 x\right) = 3$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(3 - 3 x\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(3 - 3 x\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(3 - 3 x\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(3 - 3 x\right) = 3$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(3 - 3 x\right) = 3$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(3 - 3 x\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(3 - 3 x\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(3 - 3 x\right) = \infty$$
More at x→-oo
The graph