MATH 105 Study Guide - Midterm Guide: Glassbridge Enterprises

• School: UBC
• Department: Mathematics
• Course: MATH 105
• Professor: Keqin Liu

Document Summary

1 sin2x = cos2x, 1 + tan2x = sec2x, sec2x 1 = tan2x. Double-angle formulas: sin 2x = 2sin x cos x, cos 2x = cos2x sin2x = 2cos2x 1 = 1 2sin2x. Z sec x dx = ln|sec x + tan x| + c, z csc x dx = ln|csc x + cot x| + c. Approximation"s rules and their error bound: let y = f (x) be a continu- ous function de ned on the interval [a, b] such that its derivatives f and f (4) are continuous. ) x(cid:19) x, f (a + k x) + f(cid:18)a + (k . S(n) = (f (x0) + 4f (x1) + 2f (x2) + 4f (x3) + + 4f (xn 1) + f (xn)) 3 where x = b a the midpoint rule, trapezoid rule satisfy the inequalities n . The absolute errors in approximating the integral r b a f (x)dx by. 24 ( x)2 and et k(b a)