Mister Exam
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- Limit of the function:
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Limit of (10+12*x)/x^3
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Limit of x^(3/2)*(sqrt(7+x^3)-sqrt(-1+x^3))
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Identical expressions
- eight + seven *x
- 8 plus 7 multiply by x
- eight plus seven multiply by x
- 8+7x
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Similar expressions
- 8-7*x
Limit of the function 8+7*x
The solution
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lim (8 + 7*x) x->oo
$$\lim_{x \to \infty}\left(7 x + 8\right)$$
Limit(8 + 7*x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(7 x + 8\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(7 x + 8\right)$$ =
$$\lim_{x \to \infty}\left(\frac{7 + \frac{8}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{7 + \frac{8}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{8 u + 7}{u}\right)$$
=
$$\frac{0 \cdot 8 + 7}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(7 x + 8\right) = \infty$$
$$\lim_{x \to \infty}\left(7 x + 8\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(7 x + 8\right)$$ =
$$\lim_{x \to \infty}\left(\frac{7 + \frac{8}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{7 + \frac{8}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{8 u + 7}{u}\right)$$
=
$$\frac{0 \cdot 8 + 7}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(7 x + 8\right) = \infty$$
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
$$\lim_{x \to \infty}\left(7 x + 8\right) = \infty$$
$$\lim_{x \to 0^-}\left(7 x + 8\right) = 8$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(7 x + 8\right) = 8$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(7 x + 8\right) = 15$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(7 x + 8\right) = 15$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(7 x + 8\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(7 x + 8\right) = 8$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(7 x + 8\right) = 8$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(7 x + 8\right) = 15$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(7 x + 8\right) = 15$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(7 x + 8\right) = -\infty$$
More at x→-oo
The graph