Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of (3+2*x^2+5*x)/(7+3*x+5*x^2)
-
Limit of (1+x-3*x^3+2*x^2)/(-1+x^3)
-
Limit of (2-x)^(1/(-1+x))
-
Limit of ((-1+2*x)/(2+2*x))^x
- Graphing y =:
- 2*x/7
-
Identical expressions
- two *x/ seven
- 2 multiply by x divide by 7
- two multiply by x divide by seven
- 2x/7
- 2*x divide by 7
-
Similar expressions
- (3+2*x)/(7+5*x)
- 1+((3+2*x)/(7+5*x))^x
- (x^2-2*x)/(7+x^2)
- (-84+12*x)/(7+x^2-8*x)
Limit of the function 2*x/7
The solution
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/2*x\ lim |---| x->oo\ 7 /
$$\lim_{x \to \infty}\left(\frac{2 x}{7}\right)$$
Limit((2*x)/7, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{2 x}{7}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{2 x}{7}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{7}{2} \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{7}{2} \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{2}{7 u}\right)$$
=
$$\frac{2}{0 \cdot 7} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{2 x}{7}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{2 x}{7}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{2 x}{7}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{7}{2} \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{7}{2} \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{2}{7 u}\right)$$
=
$$\frac{2}{0 \cdot 7} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{2 x}{7}\right) = \infty$$
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
$$\lim_{x \to \infty}\left(\frac{2 x}{7}\right) = \infty$$
$$\lim_{x \to 0^-}\left(\frac{2 x}{7}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{2 x}{7}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{2 x}{7}\right) = \frac{2}{7}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{2 x}{7}\right) = \frac{2}{7}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{2 x}{7}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{2 x}{7}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{2 x}{7}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{2 x}{7}\right) = \frac{2}{7}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{2 x}{7}\right) = \frac{2}{7}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{2 x}{7}\right) = -\infty$$
More at x→-oo
The graph