Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of (1-4*x)^(1/x)
-
Limit of (-16+x^2+6*x)/(-2-5*x+3*x^2)
-
Limit of (1+x)^(2/3)-(-1+x)^(2/3)
-
Limit of 1/3+x/3
- Integral of d{x}:
-
1/(2*x)
- Graphing y =:
- 1/(2*x)
- Sum of series:
- 1/(2*x)
-
Identical expressions
- one /(two *x)
- 1 divide by (2 multiply by x)
- one divide by (two multiply by x)
- 1/(2x)
- 1/2x
- 1 divide by (2*x)
-
Similar expressions
- x*(-1/2)^x
- asin((1/2)^x)
- (1+(1/2)^x)^x
Limit of the function 1/(2*x)
The solution
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1 lim --- x->oo2*x
$$\lim_{x \to \infty} \frac{1}{2 x}$$
Limit(1/(2*x), x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty} \frac{1}{2 x}$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty} \frac{1}{2 x}$$ =
$$\lim_{x \to \infty}\left(\frac{\frac{1}{2} \frac{1}{x}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{\frac{1}{2} \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(\frac{u}{2}\right)$$
=
$$\frac{0}{2} = 0$$
The final answer:
$$\lim_{x \to \infty} \frac{1}{2 x} = 0$$
$$\lim_{x \to \infty} \frac{1}{2 x}$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty} \frac{1}{2 x}$$ =
$$\lim_{x \to \infty}\left(\frac{\frac{1}{2} \frac{1}{x}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{\frac{1}{2} \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(\frac{u}{2}\right)$$
=
$$\frac{0}{2} = 0$$
The final answer:
$$\lim_{x \to \infty} \frac{1}{2 x} = 0$$
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
$$\lim_{x \to \infty} \frac{1}{2 x} = 0$$
$$\lim_{x \to 0^-} \frac{1}{2 x} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{2 x} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{2 x} = \frac{1}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{2 x} = \frac{1}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{2 x} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \frac{1}{2 x} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{2 x} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{2 x} = \frac{1}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{2 x} = \frac{1}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{2 x} = 0$$
More at x→-oo
The graph