MATH 101 Final, Spring 2004

American University of Beirut Math 101 Dr. H. Yamani Final Exam Spring 2004 Name: Do all of the following problems. Show all your work. No work shown. No credit. **** GOOD LUCK**** 1. Use the definition of limit to prove that lim,_,,(4x-2) =6 2. Find equations for the lines that are tangent to the given curve at the given point. yr y =4x4+y at (2,1) 3. Use the Mean Value theorem for f(x) = x’+ 1 on any interval [a, b] to prove that atb 2 there exists a value “c”’ such that ¢ = 4. Use the linear approximation of f(x) =Vx+1 at x= 8 to approximate V9.1. 5. The recursion formula for Newton’s method is given by eric f (%,) Given f(x}=x? —2, x, =1. Calculate successive terms x,,%),%;. What number is being approximated. 6. Evaluate the integral: nig f sec’ x 3 dx gd+ Tran x)° 7. Use the disk method to find the volume of the solid generated by revolving the region bounded by graph of x = y? +land the line x =3 about the line x =3. 8. Use the washer method to find the volume of the solid generated by revolving the region bounded by y= x? and y=2x about the y-axis . 9. Use the shell method to find the volume of the solid generated by revolving the region bounded by y =2x-x°* and the x-axis about the linex =—-1. 10. Find the area of the region bounded between the curve f(x) = x? 42x and g(x) =—x+4 in the interval [- 4, 2]. 11. Find the length of the curve y= [v3r*-1 df on-2<x<-1.