Full working out please

Full working out please

I think that i need to use a maclaurin series, but i dont understand how to go about this, if anyway could help, i would appreciate.

i need to turn xy = yx into a y = version so that i can take its derivative. how would i go about this?

For my homework i am to write 5^x^3 as a power of e. how do i go about doing this?

Calculate the Laplace Transform of the function f(t)=1

Calculate the Laplace Transform of the function f(t)=0

dy/dx | x= 1/4 =?

Consider the trapezoidal tank below with bottom length 4 m, top length 12 m, width 5 m, and height 4 m. It is lled with water, which has a density of 1000 kg/m3. Water is pumped out of a 1 m spout...

∫(x^2)/((16-x^2)^(3/2))dx I keep on getting the wrong answer.

∫(√x^2-81)/(x^4)dx I can't seem to figure out this problem. Please help.

I'm suppose to use partial fractions, and I'm given the hint: "Each denominator contains a repeated irreducible quadratic factor".

I'm given the hint: "Make a substitution before using partial fraction decomposition". edit: squared the denomenator

Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer...

Find the Taylor or Maclaurin polynomial Pn(x) for the function f with the given values of c and n. Then give a bound on the error that is incurred if Pn(x) is used to approximate f(x) on...

A dairy is planning to introduce and promote a new line of organic ice cream. After test marketing the new line in a large city, the marketing research department found that the demand in that city...

f(x)=x3−75x−1

Needing help with an integration by parts problem. A hint was given with the problem as follows, "sqrt(1-x^2)=sqrt((1-x)(1+x)).

lim x-->3 (1/x-1/3)/(x-3)

how do you find the limit at x approaches 0 of (sin(4x)/sin(7x) without using lhospital rule

send me the answer in step by step and the final solutions, please.

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