Recent content by zjhok2004

That is the definition of the little o notation

f=o(g) as x -> 0 means lim f/g ->0 as x ->0

Homework Statement Given two functions f and g with derivatives in some interval containing 0, where g is positive. Assume also f(x) = o(g(x)) as x → 0. Prove or disprove each of the following statements: a)∫f(t) dt = o(∫g(t)dt) as x → 0 (Both integrals goes from 0 to x) b)derivative of...

Solved, thanks!

But how do I able to obtain the number r?

Homework Statement obtain the number r = √15 -3 as an approximation to the nonzero root of the equation x^2 = sinx by using the cubic Taylor polynomial approximation to sinxHomework Equations cubic taylor polynomial of sinx = x- x^3/3!The Attempt at a Solution Sinx = x-x^3/3! + E(x) x^2 =...

I think you have to prove by using induction

let b denote a fixed positive integer. Prove the following statement by induction: for every integer n≥0, there exist nonnegative integers q and r such that n= qb+r, 0≤r<b. Can someone help me on how to solve this question? and how does induction works here? thank you