MAT206-981 Final Examination

MAT206-981 Final Examination Prof. Krishnamachari Answer all questions. Show complete work to get full credit. This exam is due by 10 P.M Friday, December 21, 2012 1) a) Find the value of 3 5 log 125 b) Write the following expression in condensed form 2 2 2 32 121 4 log log log 11 16 5 ? ? 2) Write each expression in expanded form a) 2 2 5 ( 1) log ( 1) 7 3 x x x x ? ? ? b) 5 2 5 ln x yz 3) Find the domain of each function : a) g(x) = log(x2 ? x) 21 ) ( ) log 1 b f x x ? ? ? ? ? ? ? ? 4) Solve the given expression and give your answer correct to three decimal places 6119 7 14 x e ? ? 5) Solve for x: a) 4 4 log x ? log (6x ?10) ?1 b) 2 log(x ?144) ?log(x ?12) ?1 6) a) Given sin 13 ? ? and cos ? ? 0 find the exact value of the remaining trigonometric functions of ? using identities. b) Find the exact value of 19 tan 6? 7) Find exact values without using a calculator a) 1 1 cot[sin ] 3 ? ? ? ?? ? ? ? b) 1 3 csc[cos ( ] 2 ? ? ? ?? ? ? ? ? ? 8) a) Solve the equation 2 4cos ? ?1, 0 ?? ? 2? b) Find all solutions of the equation 2 sec x ?sec x ? 2 in the interval, 0 ?? ? 2? 9) a) Simplify : 3 cos( ) 2? ? ? b) Establish the identity: cos sin sin cos 1 tan 1 cot ? ? ? ? ? ? ? ? ? ? ? 10) Sketch the graph of the following function over the interval [?2? ,2? ]. Indicate the amplitude, period, and phase shift. (Include a table of values) f(x) = sin ( ) 4 x ? ? 11) Extra Credit (optional) (10 points) Find the domain, x-intercept, and vertical asymptote of the logarithmic function and sketch its graph. (Include a table of values) f(x) = 5 log (x ?1) ? 4