MATH 203 Final, Summer 2005

i Math 203 Final Exam Dr. Hossam Yamani Summer 2005 ~* Name: Do each of the following problems. Show all your work. No work shown. No Credit. ***GOOD LUCK*** 1. (Please answer on page 1 of the booklet) Solve the given system of equations using Gauss-Jordan elimination method only (8 pts) —2x, +X, +3x, =-7 x, 4x, +2x, =0 x, —3x, +x, =1 2. (Please answer on page 2 of the booklet) Determine the domain and Range of the given function: (8 pts) 1 as re, 3, (Please answer on page 3 of the booklet) Determine the composite function fog = f' (g(x)) and its domain where S(aj=— g(x)=V5—x (8 pts) x? -2 4. (Please answer on page 4 and use the graph paper of the booklet) Sketch each of the following functions: (3 pts each) S(xj=—x? +4x-5 g(xja-x 4x? 4x-1 h(x) =e" +1 5. (Please answer on page 5 of the booklet) Solve for x: (8 pts) e* +10e* 7 =1 6. (Please answer on page 6 of the booklet) Solve for x , check your answer: (8 pts) logy (x + 3)+ log,, x =1 7. (Please answer on page 7 of the booklet) Determine the following limits if they exist, Explain: (5 pts each) vx42-2 x a. lim 190 lim x a 8. (Please answer on page 8 of the booklet) Determine if the given function is continuous atx =1 or not. Justify your answer. (8 pts) 2x? if x<1 x+1 if x>1 fo)=4 9. (Please answer on page 9 of the booklet) Determine all vertical and horizontal asymptotes if any of: (8 pts) 2x? —5 x+2x? f(x) = 10. (Please answer on page 10 of the booklet) Find the derivative of f(x) =x°+2x+1 using the limit approach only. (8 pts) 11. (Please answer on page 11 of the booklet) The curve y= ax’ +bx+c passes through the point (1,2) and is tangent to the line y = x at the origin. Find a, b, and c. (8 pts) 12. (Please answer on pages 12, 13, and 14 of the booklet) For each of the following functions find the first derivattve: (3 pts each) 3x-5 x)= B(x) 2x+1 h(x) =(Inx +1) (e* ~x?) x-2/) x)= Wf 22)