Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-1+e^(3*x))/x
-
Limit of sin(8*x)/x
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Limit of cot(3*x)/cot(5*x)
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Limit of (sin(x)+sin(3*x))/(10*x)
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Identical expressions
- fifty-four *x
- 54 multiply by x
- fifty minus four multiply by x
- 54x
-
Similar expressions
- 5*4^x-2^(2*x)/3
- 5*4^x+(-2)^(-x)*(2^x+4^x)
- (2^x+4^x)/((-2)^x+5*4^x)
Limit of the function 54*x
The solution
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lim (54*x) x->oo
$$\lim_{x \to \infty}\left(54 x\right)$$
Limit(54*x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(54 x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(54 x\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{54} \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{54} \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{54}{u}\right)$$
=
$$\frac{54}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(54 x\right) = \infty$$
$$\lim_{x \to \infty}\left(54 x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(54 x\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{54} \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{54} \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{54}{u}\right)$$
=
$$\frac{54}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(54 x\right) = \infty$$
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
$$\lim_{x \to \infty}\left(54 x\right) = \infty$$
$$\lim_{x \to 0^-}\left(54 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(54 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(54 x\right) = 54$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(54 x\right) = 54$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(54 x\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(54 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(54 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(54 x\right) = 54$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(54 x\right) = 54$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(54 x\right) = -\infty$$
More at x→-oo
The graph