Prove the following integrals. a) z l 0 sin nï l x sin mï l x dx = 0 if n 6= m l 2 if n = m
b) z l 0 cos mï l x dx = l if m = 0 0 if n ⥠1
c) z l 0 cos nï l x cos mï l x dx = 0 if n 6= m l 2 if n = m
d) z l âl cos nï l x cos mï l x dx = 0 if n 6= m l if n = m
e) z l âl sin nï l x sin mï l x dx = 0 if n 6= m l if n = m
f) z l âl sin nï l x cos mï l x dx = 0 for all n, m ⥠1

Answer the following for 896.31 cm= km 100cm = 1m 1000m = 1km a) 0.0089631 b) 0.0089631 c) 8.9631 d) 89.631

Billy plotted −3 4 and −1 4 on a number line to determine that −3 4 is smaller than −1 4 is he correct? explain why or why not?

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)