Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of (-3+sqrt(1+4*x))/(-2+x)
-
Limit of x^2+(sqrt(1+3*x)-sqrt(1-2*x))/x
-
Limit of ((11+7*x+7*x^2)/(14+9*x+13*x^2))^(4*x)
-
Limit of (-1+x+6*x^2)/(1/2+x)
- Factor polynomial:
- x-3*x^2
- Derivative of:
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x-3*x^2
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Identical expressions
- x- three *x^ two
- x minus 3 multiply by x squared
- x minus three multiply by x to the power of two
- x-3*x2
- x-3*x²
- x-3*x to the power of 2
- x-3x^2
- x-3x2
-
Similar expressions
- x+3*x^2
Limit of the function x-3*x^2
The solution
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/ 2\ lim \x - 3*x / x->oo
$$\lim_{x \to \infty}\left(- 3 x^{2} + x\right)$$
Limit(x - 3*x^2, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(- 3 x^{2} + x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(- 3 x^{2} + x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{-3 + \frac{1}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{-3 + \frac{1}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{u - 3}{u^{2}}\right)$$
=
$$\frac{-3}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(- 3 x^{2} + x\right) = -\infty$$
$$\lim_{x \to \infty}\left(- 3 x^{2} + x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(- 3 x^{2} + x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{-3 + \frac{1}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{-3 + \frac{1}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{u - 3}{u^{2}}\right)$$
=
$$\frac{-3}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(- 3 x^{2} + x\right) = -\infty$$
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
$$\lim_{x \to \infty}\left(- 3 x^{2} + x\right) = -\infty$$
$$\lim_{x \to 0^-}\left(- 3 x^{2} + x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- 3 x^{2} + x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- 3 x^{2} + x\right) = -2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- 3 x^{2} + x\right) = -2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- 3 x^{2} + x\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(- 3 x^{2} + x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- 3 x^{2} + x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- 3 x^{2} + x\right) = -2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- 3 x^{2} + x\right) = -2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- 3 x^{2} + x\right) = -\infty$$
More at x→-oo
The graph