Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of 2^(-n)*2^(1+n)
- Limit of tan(k*x)/x
-
Limit of (-x+tan(x))/(x+2*sin(x))
-
Limit of asin(5*x)/tan(3*x)
- Integral of d{x}:
-
4*x
- Derivative of:
-
4*x
- 4*x
-
Identical expressions
- four *x
- 4 multiply by x
- four multiply by x
- 4x
Limit of the function 4*x
The solution
You have entered
[src]
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:
$$\lim_{x \to \infty}\left(4 x\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{4} \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{4} \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{4}{u}\right)$$
=
$$\frac{4}{0} = \infty$$
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:
$$\lim_{x \to \infty}\left(4 x\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{4} \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{4} \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{4}{u}\right)$$
=
$$\frac{4}{0} = \infty$$
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