# 1 or x

1. ### lim (cos x )^(1/x ) when x = 0

here's my working , is it correct ?
2. ### How does the series 1/x diverge?

how does this diverge? how does the summation of 1/x from x=1 to infity diverge? is it just me or does this seem weird to anyone else? i assumed that as x increases, x is basically 0 (appraoching 0), so there would be a limit. \sum_{x=1}^{\infty} \frac{1}{x}
3. ### Taylor series 1/x, a=5

$$1/x, a=5 \\ \sum_{n=0}^\infty (-1)^n{(x-5)^n\over 5^{n+1}}$$ I almost had the same answer, but I don't understand where $n!$ went in the denominator (I still have it in my answer)?
4. ### Random walk with 1/(1+x) probability

You are walking along the x axis and you start at x = 0. At each time step you move to x + 1 with probability p = \frac{1}{1+x} and to x-1 with probability p = \frac{x}{1+x}. What is the expected number of steps until you return to 0 for the first time?
5. ### Area under 1/x proof

Hi, The question I am trying to solve is as follows: Let n be a positive integer greater than 1. The area of the region under the curve y=1/x from x=n-1 to x=n is between the areas of two rectangles. Show that e^-(n/(n-1)) < (1-(1/n)^n < e^-1. As far as I can tell, is I begin by...
6. ### explain why 1/x has no loc max or loc min

I know this is pretty basic, $$\frac{d}{dx} (1/x)=-x^{-2}\\ -x^{-2}=0$$ but what do we say at this point, rigorously?
7. ### Sequential definition of a limit to show limit as x goes to 0 of 1/x does not exist

Show that $\lim_{x \rightarrow 0} \frac{1}{x}$ does not exist. Is my following argument correct? I will show there exists a sequence $(x_n) \subset \mathbb{R} \backslash \{0\}$ satisfying $x_n \neq 0$ and $(x_n) \rightarrow 0$, but $\lim_{n \rightarrow \infty} f(x_n)$ does not exist...
8. ### integration of 1/x

can i change the above expression to the below expression? why?
9. ### Find the set of real numbers where x is not 0 such that 2x + 1/x < 3

Find the set of real numbers where x is not 0 such that (2x) + (1/x) < (3) So I rearrange for (2x) + (1/x) - (3) < (0) but have no idea where to go next. Any tips?
10. ### X, Y, Z are coprime integers. 1/x + 1/y = 1/z. Prove that (X+Y) is a square number.

Okay, so I'm stuck on this for an hour now, so I'd really appreciate some help, please: X, Y, Z are coprime integers. We also know that 1/x + 1/y = 1/z. Prove that (X+Y) is a square number. ----- This should be entry level university math, but I'm stuck with it. I hope I posted to the right...
11. ### Epsilon Delta 2 - (1/x)

I have been working at epsilon delta problems for hours each day and I can do many of them, but this one is destroying me and I'm tapping out for help now. f(x) = 2 - (1/x) Find d such that if 0 <|x-1|< d then |f(x)-1|< 0.1 My work is this: |2-(1/x)-1| = |1-(1/x)| = |(x/x)-(1/x)| =...
12. ### Proof that lim x-> inf (x ^ (1/x)) = 1

I started this proof by letting f(x) = (x ^ (1/x)) - 1 and attempting to show that that converges to zero. It's pretty straightforward to establish that a limit exists--x > e^1 => f(x) > 0 and f'(x) < 0, so f is bounded below and decreasing. Now what? Should I try lim inf, knowing that the...
13. ### Prove that lim x->inf (x ^ (1/x)) = 1

"Prove that lim x->inf (x ^ (1/x)) = 1." I'm stuck on this. I was able to show that the limit exists, is finite, and therefore unique. But showing that it equals 1 is eluding me. If I raise both sides to the xth power, I get x = 1^x, which is clearly wrong. So what do I do to show that the...
14. ### The derivative of 1/x

Hi. I'm having problems understanding \frac{dy}{dx}\(\frac{1}{x}) I always get 0 when I try to solve it with conventional algebra but the answer is \frac{-1}{x^2} Bonus question: How do I get the enclosing brackets in my tex code to cover \frac{1}{x} completely, instead of being small? Also...
15. ### Integral of (2x+1)/(x+2)^2 dx

I need to solve Integral of (2x+1)/(x+2)^2 dx I would like to know how its throughly been done step by step, but before that I would atleast like to show you my progress even if it's a bit incorrent. The important thing is trying, but if someone could show me to complete steps I would be...
16. ### USING YOUR COMPASS ONLY, construct a point on a number line that equals 1/x

_____0_________________________1______________x 1/x=??
17. ### Expected Value of 1/X

Hey there. I've been messing around with some of the statistics involved with dice rolls, particularly in the context of tabletop roleplaying games, but I've come to a snag. Mainly due to my incredibly shaky knowledge of statistics. An elementary method which players of a game use to 'guess'...
18. ### What is the derivative of this function, f(x)= [(x^2+3x+1)/(x+1)}?

What is the derivative of this function, f(x)= [(x^2+3x+1)/(x+1)}?
19. ### What is the Maclaurin series of 1/(x+1)^0.5?

Does anyone know what the Maclaurin series of 1/\sqrt{x+1} is?
20. ### to draw y = 1/x

come when you draw y = 1/x you dont see x values plotted on the -tve side of x?