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