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))
- Graphing y =:
- 10*x^2
- Derivative of:
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10*x^2
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Identical expressions
- ten *x^ two
- 10 multiply by x squared
- ten multiply by x to the power of two
- 10*x2
- 10*x²
- 10*x to the power of 2
- 10x^2
- 10x2
-
Similar expressions
- (-6-x+10*x^2)/(-x^3+3*x)
- (1+10*x)^(2+1/x)
Limit of the function 10*x^2
The solution
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/ 2\ lim \10*x / x->oo
$$\lim_{x \to \infty}\left(10 x^{2}\right)$$
Limit(10*x^2, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(10 x^{2}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(10 x^{2}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{10} \frac{1}{x^{2}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{10} \frac{1}{x^{2}}} = \lim_{u \to 0^+}\left(\frac{10}{u^{2}}\right)$$
=
$$\frac{10}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(10 x^{2}\right) = \infty$$
$$\lim_{x \to \infty}\left(10 x^{2}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(10 x^{2}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{10} \frac{1}{x^{2}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{10} \frac{1}{x^{2}}} = \lim_{u \to 0^+}\left(\frac{10}{u^{2}}\right)$$
=
$$\frac{10}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(10 x^{2}\right) = \infty$$
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
$$\lim_{x \to \infty}\left(10 x^{2}\right) = \infty$$
$$\lim_{x \to 0^-}\left(10 x^{2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(10 x^{2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(10 x^{2}\right) = 10$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(10 x^{2}\right) = 10$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(10 x^{2}\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(10 x^{2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(10 x^{2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(10 x^{2}\right) = 10$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(10 x^{2}\right) = 10$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(10 x^{2}\right) = \infty$$
More at x→-oo
The graph