Recent content by wimma

Homework Statement I'm reading a book where they do the following steps which I don't understand: We have a DE: b^2 * y'' = axy put t = b^(-2/3) a ^(1/3) x then somehow get (d^2 y)/dt^2 = ty how? Homework Equations None. The Attempt at a Solution I tried messing with chain...

but won't the parameter go to -infinity so we can't equate (1+1/x)^x to e?

Homework Statement Find the limit as n--> infinity of (1-2/n)^n Homework Equations We know (1+1/x)^x --> e as n--> infinity The Attempt at a Solution I worked it out as e^(-2) using log but I can't get it out using the fundamental limit above. I know it's the square of (1-1/x)^x...

Homework Statement Solve the recursive function: A_{n+1} = (8/9)A_{n} + (24/9)*(20/9)^n We want a closed formula for A_n Homework Equations I'm just doing this to work out the surface area of the Menger Sponge. I know the formula's probably out there, but I get this...

cheers =] i got the result i'm looking at trying to do the same problem with taylor polynomials... i get the taylor polynomial for sin ^2 (x) to be \sum{\frac{-(-1)^k 2^{2k-1}x^{2k}}{(2k)!}} ... inverting this to get the one for cosec ^2 (x) looks a bit mean.

so i do it four times and get \lim{x \rithgtarrow 0} \left( \frac{-4 cos (2x)}{-20 sin (2x) + 16 cos (2x) - 4 x ^ 2 cos (2x)} \right)

yeah cos i gave up before i finished the denominator fix'd

yeah we've learned taylor polynomials. i guess i could make a taylor polynomial of appropriate degree for each one, though the question says to use l'hospitals. i went \lim_{x \rightarrow 0} \left( \frac{1}{x ^ 2} - \frac{1}{\sin ^ 2 x} \right) = \lim_{x \rightarrow 0} \left( \frac{\sin ^ 2...

Homework Statement lim as x tends to zero of (x^(-2) - (cosecx)^2) Homework Equations L'Hospital's rule The Attempt at a Solution I keep getting things in the denominator that won't go away no matter how much I differentiate. I'm missing something here...

Updated

Sorry about that

Homework Statement (a) Give Taylor Polynomal of order 4 for ln(1+x) about 0. (b) Write down Tn(x) of order n by looking at patterns in derivatives in part (a), where n is a positive integer. (c) Write down the remainder term for the poly. in (b) (d) How large must n be to ensure Tn gives a...

Homework Statement P is a polyhedron defined by (+/-) x (+/-) z <= 1 (+/-) x (+/-) y <= 1 (+/-) y (+/-) z <= 1 These are 12 inequalities with every possible sign choice taken. Is P a regular polyhedron? If so, which type? Homework Equations If we change one inequality to an...

Thanks for your help, though I don't understand how you got that answer... We go f_beat = f_receive - f_transmit and when I substitute in I get the wrong answer... your answer was correct by the way. Could you please put in your substitution steps? Thanks

MasteringPhysics still fails me on that answer Note: I compute 280.296 m/s Why would it be that order of magnitude? (Other than common sense to do with a bat)