Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-6+x^2-x)/(6+x^2-5*x)
-
Limit of log(1+x^2)/(-e^(-x)+cos(3*x))
-
Limit of -2+|-2+x|/x
-
Limit of (-4-8*x+8*x^2)/(3+8*x)
- Graphing y =:
- x^2-5*x
- Factor polynomial:
- x^2-5*x
-
Identical expressions
- x^ two - five *x
- x squared minus 5 multiply by x
- x to the power of two minus five multiply by x
- x2-5*x
- x²-5*x
- x to the power of 2-5*x
- x^2-5x
- x2-5x
-
Similar expressions
- x^2+5*x
- (-10+x^2-5*x)/(-25+x^2)
- (4+x^2-5*x)/(-3+x^2+2*x)
- (4-x)/(4+x^2-5*x)
Limit of the function x^2-5*x
The solution
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/ 2 \ lim \x - 5*x/ x->oo
$$\lim_{x \to \infty}\left(x^{2} - 5 x\right)$$
Limit(x^2 - 5*x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(x^{2} - 5 x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(x^{2} - 5 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 - \frac{5}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 - \frac{5}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{- 5 u + 1}{u^{2}}\right)$$
=
$$\frac{\left(-5\right) 0 + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{2} - 5 x\right) = \infty$$
$$\lim_{x \to \infty}\left(x^{2} - 5 x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(x^{2} - 5 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 - \frac{5}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 - \frac{5}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{- 5 u + 1}{u^{2}}\right)$$
=
$$\frac{\left(-5\right) 0 + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{2} - 5 x\right) = \infty$$
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
$$\lim_{x \to \infty}\left(x^{2} - 5 x\right) = \infty$$
$$\lim_{x \to 0^-}\left(x^{2} - 5 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} - 5 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} - 5 x\right) = -4$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} - 5 x\right) = -4$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} - 5 x\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x^{2} - 5 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} - 5 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} - 5 x\right) = -4$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} - 5 x\right) = -4$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} - 5 x\right) = \infty$$
More at x→-oo
The graph