Write the Maclaurin’s series for f(x)=sin(3x)+e^x up to the third order

 To simplify this question, it is possible to expand the two elements of the function and then add the two expansions together.First, the expansion of sin(3x) around the origin is sin(30)+d/dx sin(3x)+d²/dx² sin(3x)+d³/dx³ sin(3x)=sin(30)+3cos(30)x-33sin(30)x²/2!-333cos(3*0)*x³/3!+…=0+3x+0x²-27x³/3!+…=0+3x+0x²-9x³/2+… (1)Then, the expansion of e^x is trivial as 1+x+x²+x³… (2) and can be added to our previous result (1), obtaining the final result: f(x)=1+4x+x²/2-25x³/6+…

TD
Answered by Tutor294323 D. Further Mathematics tutor

3252 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Prove that (AB)^-1 = B^-1 A^-1


Find the eigenvalues and eigenvectors of the matrix M , where M{2,2} = (1/2 2/3 ; 1/2 1/3) Hence express M in the form PDP^-1 where D is a diagonal matrix.


Find the eigenvalues and corresponding eigenvectors of the following matrix: A = [[6, -3], [4, -1]]. Hence represent the matrix in diagonal form.


Integrate xcos(x) with respect to x


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences