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