# Search results

1. ### Question about graphing L(x,y) against f(x,y)

The question I'm stuck on is this: Let f(x,y) = (x+1)^2 + y^2 I'm asked to find the partial derivatives and then evaluate them at (1,2). From there, find L(x,y), the linear approximation to f(x,y) at (1,2). That part I'm ok with. I got the following: f_x(x,y) = 2(x+1) f_y(x,y) = 2y...
2. ### Testing for convergence/divergence

Thanks for the replies. It's helped me get my head around these problems better. I like jbunniii's solution. very clever and succinct. For this question: \lim_{n \to \infty} \frac {n^p}{a^n} = 0 my solution is: Apply L'Hopital's Rule: \frac{p}{ln(a)} [\lim_{n \to \infty} \frac...
3. ### Testing for convergence/divergence

I've got a couple of problems I'm stuck on. Any help gratefully received! Test for convergence/divergence: \sum_{n=1}^{\infty} \frac {(n+1)}{n^3 ln(n+2)} What test should I do here? Can I rearrange the equation to be: \frac{(\frac{1}{n^2} + \frac{1}{n^3})}{ln(n+2)} and then use...

15. ### Maximum area/volume problems

D'oh! I meant 12cm^{2} not 24. thanks for spotting that error. And thanks for the advice on Q2.
16. ### Maximum area/volume problems

[SOLVED] Maximum area/volume problems I have two here. One I feel I've solved but am just looking for reassurance (I'm needy that way!), The other I've got an answer but I know I've missed something. Homework Statement 1. A rectangle is inscribed in a 6/8/10 cm right-angle triangle where two...
17. ### Maxima/Minima problem

By that I assume you mean this: 72x^3-16x+45) = 4x^2(18x^3-12x+15) If so, expand back out. the two sides don't match up. That would indicate a flat spot then, not a max/min point. You can find that out by checking to see if the signs on f''(x) change at that point. If they don't then it isn't...
18. ### Maxima/Minima problem

You really need to recheck your work there. Your f'(x) is correct as far as I can see, but not when you reduce it to x^2(18x^3-12x+15). Expand it out and you get a much different answer to your first one of f'(x). Also, your f''(x) is wrong. 72x^5 differentiated doesn't equal 288x^3 Nor does...
19. ### Finding points of inflection

the graph x4 - 4x2 is the second derivative, not f(x).
20. ### Finding points of inflection

third derivative is 4x^{3}-8x solving for f'''(x) = 0 gives us x = +/-\sqrt{2} and x = 0. minima points of f''(x) are at x = (-\sqrt{2}, -4) & (\sqrt{2}, -4) maxima point of f''(x) is (0, 0). I still confused here! How does this help me find the y co-ordinates for inflection points of...
21. ### Finding points of inflection

Homework Statement Suppose the graph f''(x) of a function is given by: (see attachment) (a) Find all points of inflection of f(x) The Attempt at a Solution First I figured, by looking at the graph and seeing the intercept points [(-2,0),(0,0),(2,0)] that f''(x) = x^{4}-4x^{2} solving for...
22. ### Differentiation help

Right, I think I'm getting on okay with these. Thanks for all the help. I'm still having issues with c though. I tried doing it a different way: Now correct me if I'm wrong but: cos^{4}(t^{2} + e^{2t}) can be written as (cos(t^{2} + e^{2t}))^{4} right? (please say it is!) And then...
23. ### How is this probability reasoning wrong?

I think the problem here is that Francis is getting confused between dependent vs independent probability. (sorry there's prob a better way to say that but that's the best I can come up with!) By this I mean that he (assuming Francis is a he) is correct in saying the probability of the next...
24. ### How is this probability reasoning wrong?

What would be the probability of the 3rd sock being light if you only have 1 pair of each colour - and the first two socks you pulled out were light?
25. ### How ould I start this off?

Maybe drawing it 1st will give you an idea of what the equation should be. A line of inlcination 180\cdot going through (0,2) would have the equation: y = 2
26. ### Differentiation help

Well I did say I was very rusty! okay, looking at them again I think where I'm going wrong is that I just differentiating parts seperately, so not using the Product rule correctly. Is that fair to say? For a), Is this closer to the answer: (x-2)^{3}.-2e^{-2x} + 3(x-2)^{2}.e^{-2x} and then...
27. ### Differentiation help

Help please on these. I'm extremely rusty with differentiation and want to know if I've got the right answers here Homework Statement differentiate the following functions (you do not have to simplify): a. f(x)=(x-2)^{3}e^{-2x} b. f(x) = cos x / ln (x^{2} + x) c. g(t) = cos^{4}(t^{2} +...
28. ### System of equations problem

solving the second equation is easy enough - just make y the subject. As for the first, I find it's easier to rewrite it without using negative powers. x^{-2/3} = \frac{1}{x^{2/3}} From there, it's just a matter of rearranging to make y the subject again. From there, you can find x...
29. ### Math 30 pure geometric series

A. Think about it for a second: If each successive swing is less than the one prior, then how could the 10th swing be 11 feet more than the 1st? Looks to me like you've got the total sum of the ten swings, not the length of the 10th. B. We know that the 1st swing is 2 foot. Each...
30. ### How do I work this out?

minor quibble, but you should really write that as ln(1.08), not ln1+0.08, as it does make it look like you're wanting to multiply t by the ln of 1 and then add 0.08. If you did this, you're answer would end up being out by a little over 8%.