Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-1+3*sqrt(x))/(-1+4*sqrt(x))
-
Limit of (-4+2*x)/(6+4*x+7*x^2)
-
Limit of ((5+2*x)/(2*x))^(3*x)
-
Limit of ((-4+2*x)/(1+2*x))^(5+3*x)
- Graphing y =:
- 3*x/4
-
Identical expressions
- three *x/ four
- 3 multiply by x divide by 4
- three multiply by x divide by four
- 3x/4
- 3*x divide by 4
-
Similar expressions
- (3*x/(4+3*x))^(2+7*x)
- (-4+x^2+3*x)/(4+x)
- (1-2*x^2+3*x)/(4+x^2-3*x)
- (2+x^2-3*x)/(4+x^2-4*x)
- sin(4*x)*tan(3*x)/(4*x^2)
Limit of the function 3*x/4
The solution
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/3*x\ lim |---| x->oo\ 4 /
$$\lim_{x \to \infty}\left(\frac{3 x}{4}\right)$$
Limit((3*x)/4, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{3 x}{4}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{3 x}{4}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{4}{3} \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{4}{3} \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{3}{4 u}\right)$$
=
$$\frac{3}{0 \cdot 4} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{3 x}{4}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{3 x}{4}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{3 x}{4}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{4}{3} \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{4}{3} \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{3}{4 u}\right)$$
=
$$\frac{3}{0 \cdot 4} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{3 x}{4}\right) = \infty$$
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
$$\lim_{x \to \infty}\left(\frac{3 x}{4}\right) = \infty$$
$$\lim_{x \to 0^-}\left(\frac{3 x}{4}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{3 x}{4}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{3 x}{4}\right) = \frac{3}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{3 x}{4}\right) = \frac{3}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{3 x}{4}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{3 x}{4}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{3 x}{4}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{3 x}{4}\right) = \frac{3}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{3 x}{4}\right) = \frac{3}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{3 x}{4}\right) = -\infty$$
More at x→-oo
The graph