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