APPM 1235 Final: appm1235spring2016finalexam_sol
Document Summary
1. %%%[12%points]%%the%voltage%in%millivolts%(mv)%of%an%rc%circuit%as%a%function%of%time%in%milliseconds%(ms)%is%given%by%the% function% v (t) = 20 1 e 2t. ) %%for% t 0 . % (a)%%what%is% v (0) ?%%________________________________________% (b)%%what%voltage% v %does%the%circuit%approach%as%t%!% ?%%________________________________________% (c)%%at%what%time% t %will% v = 5 mv?% 4 (x 2)2 (x + 5)(x 4) :% (a)%%where%is% p(x) > 0 ?% (b)%%a%function% q(x) %is%defined%to%be% q(x) = 5p(x 3) . %%what%are%the%zeros%of% q(x) ?%%% 8 x 5 (a)%%at%what%values%of%x%does g(x) = 0 ,%if%any?% (b)%%state%all%the%asymptotes%(horizontal,%vertical%and/or%slant)%of% g(x) . % Page%2% x3 + log2 (x 6) = log2 16 % 6. %%%[10%points]%%set%up%and%then%simplify%the%difference%quotient% f (x + h) f (x) h. %for% f (x) = x x + 2. 7. %%%[12%points]%%a%ball%is%thrown%straight%up%from%the%top%of%128ufoot%cliff%and%falls%to%the%ground%below%the%cliff. %%the% ball"s%height%above%the%ground%in%feet%as%a%function%of%time%in%seconds%is%determined%by%the%function% h(t) = 16t 2 + 32t +128 . %%%answer%the%following%questions%giving%the%correct%units%with%your%answers. % (a)%determine%the%average%rate%of%change%of%the%height%of%the%ball%from%the%time%that%it%is%thrown%to%the%time%it%hits%the% ground. %%% (b)%%what%is%the%maximum%height%the%ball%reaches?% 11. %%find%all%solutions:%% (2 x 1)2 5(2 x 1) + 4 = 0 % E. %% (b a)2 (b + a) a2b2. 14. %%the%function% f (x) = x3 + 6x2 + 3x 10 %has%a%factor%of% (x 1) . %%find%all%the%real% zeros%of%the%function. %% ,% y = x ,% y = x x ,% y = ex.
