Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of log(sin(x))/log(sin(2*x))
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Limit of 1/(2*x^2)
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Limit of exp(-x)*log(x)
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Limit of 1/x
- How do you in partial fractions?:
- 1/(2*x^2)
- Integral of d{x}:
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1/(2*x^2)
- Derivative of:
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1/(2*x^2)
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Identical expressions
- one /(two *x^ two)
- 1 divide by (2 multiply by x squared )
- one divide by (two multiply by x to the power of two)
- 1/(2*x2)
- 1/2*x2
- 1/(2*x²)
- 1/(2*x to the power of 2)
- 1/(2x^2)
- 1/(2x2)
- 1/2x2
- 1/2x^2
- 1 divide by (2*x^2)
Limit of the function 1/(2*x^2)
The solution
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1
lim ----
x->oo 2
2*x
$$\lim_{x \to \infty} \frac{1}{2 x^{2}}$$
Limit(1/(2*x^2), x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty} \frac{1}{2 x^{2}}$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty} \frac{1}{2 x^{2}}$$ =
$$\lim_{x \to \infty}\left(\frac{\frac{1}{2} \frac{1}{x^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{\frac{1}{2} \frac{1}{x^{2}}}{1}\right) = \lim_{u \to 0^+}\left(\frac{u^{2}}{2}\right)$$
=
$$\frac{0^{2}}{2} = 0$$
The final answer:
$$\lim_{x \to \infty} \frac{1}{2 x^{2}} = 0$$
$$\lim_{x \to \infty} \frac{1}{2 x^{2}}$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty} \frac{1}{2 x^{2}}$$ =
$$\lim_{x \to \infty}\left(\frac{\frac{1}{2} \frac{1}{x^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{\frac{1}{2} \frac{1}{x^{2}}}{1}\right) = \lim_{u \to 0^+}\left(\frac{u^{2}}{2}\right)$$
=
$$\frac{0^{2}}{2} = 0$$
The final answer:
$$\lim_{x \to \infty} \frac{1}{2 x^{2}} = 0$$
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
$$\lim_{x \to \infty} \frac{1}{2 x^{2}} = 0$$
$$\lim_{x \to 0^-} \frac{1}{2 x^{2}} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{2 x^{2}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{2 x^{2}} = \frac{1}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{2 x^{2}} = \frac{1}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{2 x^{2}} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \frac{1}{2 x^{2}} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{2 x^{2}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{2 x^{2}} = \frac{1}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{2 x^{2}} = \frac{1}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{2 x^{2}} = 0$$
More at x→-oo
The graph