# 1 or x

1. ### The graph of y=x+1/x is shown on the insert. The lowest point on the branch is (1,2)

...The highest point on the other branch is(-1,-2) (i) Use the graph to solve the following equations, showing your method clearly A x+1/x=4 B 2x+1/x=4 The equation (x-1)^2 +y^2=4 represents a circle. Find in exact form the coordinates of the points of intersection of this circle with the...
2. ### Given x+(1/y)= y + (1/z) = z+ (1/x). Prove x=y=z.

This is a simple math problem. I do remember solving these in grade 9. forgot all the formulas so don't even know where to start. x+(1/y)= y + (1/z) = z+ (1/x) Prove x=y=z This is kind of urgent. Millions of thanks in advance
3. ### Uniform Continuity for 1/x

I'm trying to prove the following statement: Prove that the function f(x)=1/x is continuous on (0,1] but it is not uniformly continuous on this interval. Thanks a lot.
4. ### Where does the graph y=x+1/x+2 cross the coordinate axes?

Where does the graph y=x+1/x+2 cross the coordinate axes? Can you please explain what the question means and how to do it. Thanks
5. ### Solve y = x + 1/x with 0 \< x \< 1 for x in terms of y.

I need help with this assignment, Problem 3: Solve y = x + 1/x with 0 \< x \< 1 for x in terms of y. Any clues as to how to do this, would be greatly appreciated :)
6. ### Find a function F(x) such that F'(x)= 1/x and F(1)=2

Find a function F(x) such that F'(x)= 1/x and F(1)=2 Leave an exact answer- do not approximate any numbers This is how I got it: To fine F(x) I found the antiderivative for F'(x). The antiderivative of 1/x is equal to ln(x), because the derivative of ln(x) is 1/x. I know that the derivative...
7. ### expressing repeating fractions as integral of 1/x

EDIT: Nevermind about the "fraction" part. What I mean is a number whose last digit repeats infinitely. The function f(x)=\frac{1}{x} is not defined at x=0. What is the proper way to express numbers with an infinitely repeating last digit as the area under this function? Taking a...
8. ### Solve 2/[(x^2)-x] = (1/x) + 4/(x^2-1)

Can somebody help me solve this equation? I have gotten to a certain point then get stuck. Thank you! 2/x^2-x = (1/x) + (4/x^2-1)
9. ### integrate sin (1/x)

I'm a little lost on this one. I don't see how substitution could work because the derivative of 1/x is -1/x^2
10. ### Limit of (a^x -1)/x when x approaches 0

The answer is ln a. This was a problem we got last semester (book of exercises). We didn't have to solve this but I'm still wondering how to solve it. The tip is to substitute a^x - 1 by t. I would enter the formula in LaTeX but I haven't found yet how to enter a limit in LaTeX-code.
11. ### Show that f(x) = 1/x is continuous at x=5.

Hi, I understand thus but I'm struggling with the proof. I have so far: f(5) = 1/5 so we need to show that for all positive epsilon(E) such that that there exists positive delta(d) s.t |(1/x) - 1/5)| < E for all x satisfying |x-5|<d Then when I searched some threads on here I saw...
12. ### does 1/x in Lp

I need to check whether or not \frac{1}{x} \in {L}^p \int_{0}^{1} \frac{1}{|x|^p} ~dx = \frac{1}{-p + 1} x^{-p + 1}|_{0}^1 because this integral divergent, so \frac{1}{x} \notin {L}^p is it correct?? thanks for any comment and suggestion
13. ### Continuity of 1/x

Show that 1/x is continuous on at any c =/= 0 hint: chose delta to stay away from 0 i have a general idea of how it works but I'm not really sure how to "use delta = min{[c]/2,c^2(e/2)} "(answer from book)
14. ### Integration of 1/x

Hi, I'm not sure how to get up the integral sign with limits but the question im trying is Integrate (1 + 1/X) dx limits: a=1 b=2 I make the intgral: x + ln|x| And the answer: 1 + ln |2| But alas i'm wrong. Can anyone see where i've gone wrong?
15. ### Prove continuouty of 1/x (delta-epsilon)

Hi guys, I've been trying to do this for a while but I'm not really getting anywhere. Hints would be much appreciated! The problem Prove that the function g(x)=1/x is continuous on \mathbb{R}\smallsetminus\{0\}, but cannot be defined at the origin 0 in such a way that the resulting function...
16. ### Area of 1/x from 1 to infinity

\int_1^{\infty} \frac{1}{x} dx = \infty Why is the area infinity? I plotted the graph, and it looks like a finite amount of area from 1 to infinity as the asymptote is 0 as x approaches infinity.
17. ### (Square root of X) * (1/X) = (1/Square root of X)?

(Square root of X) * (1/X) = (1/Square root of X) Can anyone explain to me why did this is so? I take it turns into (Square root of X / X), but then what? (Headbang)
18. ### integral of 1/x

Hi, I understand that differentiate both ln x and ln |x| will give 1/x. But why \int \frac{1}{x} dx=ln|x|+c. Is it ok if I write \int \frac{1}{x} dx=ln x+c Can someone help?
19. ### problem with finding the key features of f(x) = x ln(e+1/x)

i have few math questions about function f(x)=xln(e+1/x) 1. what is value of x when f(x)=0 2. domain, extremum and asymptote of this function 3. what is the value of lim f(x) when x->0+ 4. what is the value of lim f(x) when x->(-1/e)- 5.how does this graph look like ??? please help:)
20. ### Closest Pt of y = 1/x to Origin

Hey guys Find the coordinates of the point on the graph of y = 1/x (x>0) which is the closest to the origin. Looking at a graph, the pt would b (1,1) i fink but i have not clue how i would prove it...i tried finding the turning pts like the previous problems but y = 1/x doesnt have any =p...