Mister Exam
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How to use it?
- Limit of the function:
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Limit of (2+sqrt(x)-sqrt(2))/x
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Limit of (2-x)/(-1+x)^2
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Limit of e^(x^2)-cos(x)/x^2
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Limit of (-x+3*x^2)/(5+x^2)
- Integral of d{x}:
- -7-x
-
Identical expressions
- - seven -x
- minus 7 minus x
- minus seven minus x
-
Similar expressions
- 7-x
- -7+x
- -acot(x)+100*x-7^(-x)*tan(x)/2
Limit of the function -7-x
The solution
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lim (-7 - x) x->oo
$$\lim_{x \to \infty}\left(- x - 7\right)$$
Limit(-7 - x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(- x - 7\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(- x - 7\right)$$ =
$$\lim_{x \to \infty}\left(\frac{-1 - \frac{7}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{-1 - \frac{7}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{- 7 u - 1}{u}\right)$$
=
$$\frac{-1 - 0}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(- x - 7\right) = -\infty$$
$$\lim_{x \to \infty}\left(- x - 7\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(- x - 7\right)$$ =
$$\lim_{x \to \infty}\left(\frac{-1 - \frac{7}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{-1 - \frac{7}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{- 7 u - 1}{u}\right)$$
=
$$\frac{-1 - 0}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(- x - 7\right) = -\infty$$
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
$$\lim_{x \to \infty}\left(- x - 7\right) = -\infty$$
$$\lim_{x \to 0^-}\left(- x - 7\right) = -7$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x - 7\right) = -7$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x - 7\right) = -8$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x - 7\right) = -8$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x - 7\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(- x - 7\right) = -7$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x - 7\right) = -7$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x - 7\right) = -8$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x - 7\right) = -8$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x - 7\right) = \infty$$
More at x→-oo
The graph