FormulaPage - You may find the following expressions...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: You may find the following expressions useful. And you may not. But you may use them if they prove useful. “Known” Taylor series (all around x = 0): x3 (−1)n x2n+1 + ··· + + ··· 3! (2n + 1)! x2 (−1)n x2n cos(x) = 1 − + ··· + + ··· 2! (2n)! xn x2 + ··· + + ··· ex = 1 + x + 2! n! p(p − 1) 2 p(p − 1)(p − 2) 3 (1 + x)p = 1 + px + x+ x + ··· 2! 3! sin(x) = x − “Known” integral expressions: 1 1 xn ln x dx = xn+1 ln x − xn+1 + C n+1 (n + 1)2 1 eax (a sin(bx) − b cos(bx)) + C eax sin(bx) dx = 2 a + b2 1 eax (a cos(bx) + b sin(bx)) + C eax cos(bx) dx = 2 a + b2 1 sin(ax) sin(bx) dx = 2 (a cos(ax) sin(bx) − b sin(ax) cos(bx)) + C, b − a2 1 cos(ax) cos(bx) dx = 2 (b cos(ax) sin(bx) − a sin(ax) cos(bx)) + C, b − a2 1 sin(ax) cos(bx) dx = 2 (b sin(ax) sin(bx) + a cos(ax) cos(bx)) + C, b − a2 a=b a=b a=b “Known” equations from geometry: Volume of a sphere: V = Surface area of a sphere: 4 π r3 3 A = 4π r2 Volume of a cylinder: V = π r2 h 1 Volume of a cone: V = π r2 h 3 1 ...
View Full Document

This note was uploaded on 01/28/2012 for the course MATH 116 taught by Professor Irena during the Fall '07 term at University of Michigan.

Ask a homework question - tutors are online