# Spring 2018 Exam 3.pdf - Math 172 Spring 2018 Exam 3 This...

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Math 172 Spring 2018Exam 3This 100 point exam has 8 questions. Numbers in the [ ] tell what each problem is worth. Unsimplified answersare generally okay, though we might take a point for leaving things like cos(π) or ln(1) ore0.Show work orexplanation on everything. Show all relevant work on the exam pages (extra attached pages will not be scanned).Lab Section:Identities:sin2(x) + cos2(x) = 1sin2(x) =12[1-cos(2x)]cos2(x) =12[1 + cos(2x)]Known Maclaurin series:11-x=summationdisplayk=0xk=1+x+x2+x3+...,|x|<1ex=summationdisplayk=0xkk!=1+x1!+x22!+x33!+...,|x|<sin(x)=summationdisplayk=0(-1)kx2k+1(2k+1)!=x-x33!+x55!-x77!+...,|x|<cos(x)=summationdisplayk=0(-1)kx2k(2k)!=1-x22!+x44!-x66!+...,|x|<tan-1(x)=summationdisplayk=0(-1)kx2k+12k+1=x-x33+x55-x77+...,|x| ≤1ln(1+x)=summationdisplayk=1(-1)k-1xkk=x-x22+x33-x44+...,|x|<1(1+x)p=summationdisplayk=0parenleftbiggpkparenrightbiggxk=1+px+p(p-1)2!x2+p(p-1)(p-2)3!