Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of 1-cos(3*x)
-
Limit of ((6+5*x)/(-1+5*x))^((1+2*x^2)/x)
-
Limit of (-3*5^(1+x)+5*2^x)/(2*5^x+100*2^x)
-
Limit of (4^x-9^x)/(4^(1+x)+9^(1+x))
- Integral of d{x}:
- -x^2+3*x
- Factor polynomial:
- -x^2+3*x
-
Identical expressions
- -x^ two + three *x
- minus x squared plus 3 multiply by x
- minus x to the power of two plus three multiply by x
- -x2+3*x
- -x²+3*x
- -x to the power of 2+3*x
- -x^2+3x
- -x2+3x
-
Similar expressions
- -x^2-3*x
- (-6-x+5*x^2)/(4-x^2+3*x)
- x^2+3*x
Limit of the function -x^2+3*x
The solution
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/ 2 \ lim \- x + 3*x/ x->oo
$$\lim_{x \to \infty}\left(- x^{2} + 3 x\right)$$
Limit(-x^2 + 3*x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(- x^{2} + 3 x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(- x^{2} + 3 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{3}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{3}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{3 u - 1}{u^{2}}\right)$$
=
$$\frac{-1 + 0 \cdot 3}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(- x^{2} + 3 x\right) = -\infty$$
$$\lim_{x \to \infty}\left(- x^{2} + 3 x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(- x^{2} + 3 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{3}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{3}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{3 u - 1}{u^{2}}\right)$$
=
$$\frac{-1 + 0 \cdot 3}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(- x^{2} + 3 x\right) = -\infty$$
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
$$\lim_{x \to \infty}\left(- x^{2} + 3 x\right) = -\infty$$
$$\lim_{x \to 0^-}\left(- x^{2} + 3 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x^{2} + 3 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x^{2} + 3 x\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x^{2} + 3 x\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x^{2} + 3 x\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(- x^{2} + 3 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x^{2} + 3 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x^{2} + 3 x\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x^{2} + 3 x\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x^{2} + 3 x\right) = -\infty$$
More at x→-oo
The graph