Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-3*e^(4*x)-2*e^(-x)+5*e^(2*x))/(-4*sqrt(1+5*x)+4*cos(3*x)+5*sin(2*x))
-
Limit of (2+x^2+3*x)/(2+2*x^2+5*x)
- Limit of (-1+x)*cot(pi*(-1+x))
-
Limit of (9+x^10-10*x)/(-1+x)^2
- Derivative of:
- 30*x
- 30*x
-
Identical expressions
- thirty *x
- 30 multiply by x
- thirty multiply by x
- 30x
Limit of the function 30*x
The solution
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lim (30*x) x->oo
$$\lim_{x \to \infty}\left(30 x\right)$$
Limit(30*x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(30 x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(30 x\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{30} \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{30} \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{30}{u}\right)$$
=
$$\frac{30}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(30 x\right) = \infty$$
$$\lim_{x \to \infty}\left(30 x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(30 x\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{30} \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{30} \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{30}{u}\right)$$
=
$$\frac{30}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(30 x\right) = \infty$$
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
$$\lim_{x \to \infty}\left(30 x\right) = \infty$$
$$\lim_{x \to 0^-}\left(30 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(30 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(30 x\right) = 30$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(30 x\right) = 30$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(30 x\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(30 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(30 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(30 x\right) = 30$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(30 x\right) = 30$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(30 x\right) = -\infty$$
More at x→-oo
The graph