Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((2+x)/(4+x))^cos(x)
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Limit of -5-2*x^2+8*x
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Limit of (-9+x^2)/(-27+x^3)
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Limit of 1+7*x+11*x^2/2
- Derivative of:
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3-5*x
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Identical expressions
- three - five *x
- 3 minus 5 multiply by x
- three minus five multiply by x
- 3-5x
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Similar expressions
- 3+5*x
Limit of the function 3-5*x
The solution
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lim (3 - 5*x) x->oo
$$\lim_{x \to \infty}\left(3 - 5 x\right)$$
Limit(3 - 5*x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(3 - 5 x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(3 - 5 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{-5 + \frac{3}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{-5 + \frac{3}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{3 u - 5}{u}\right)$$
=
$$\frac{-5 + 3 \cdot 0}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(3 - 5 x\right) = -\infty$$
$$\lim_{x \to \infty}\left(3 - 5 x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(3 - 5 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{-5 + \frac{3}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{-5 + \frac{3}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{3 u - 5}{u}\right)$$
=
$$\frac{-5 + 3 \cdot 0}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(3 - 5 x\right) = -\infty$$
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
$$\lim_{x \to \infty}\left(3 - 5 x\right) = -\infty$$
$$\lim_{x \to 0^-}\left(3 - 5 x\right) = 3$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(3 - 5 x\right) = 3$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(3 - 5 x\right) = -2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(3 - 5 x\right) = -2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(3 - 5 x\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(3 - 5 x\right) = 3$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(3 - 5 x\right) = 3$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(3 - 5 x\right) = -2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(3 - 5 x\right) = -2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(3 - 5 x\right) = \infty$$
More at x→-oo
The graph