Islamic University of GazaDepartment of Math.Summer Semester 16/9/2014

Calculus BFinal ExamTime: 2hours

IQ71 Q8~'i\ Ql Q2 Q3 Q4 Q5 Q6 Total

~)I 12 10 18I 14 16

i 10 10 10I

100,

'-'I.WJJ.J \I I Ii

Solve the following questions:

[Ql] (a) Let! (x) = logx e, x > 1.

(i) Show that !-\(x) exists.

(ii)Find f -1(x ).

(b) Find y I for the function y = (sin-1 x r -(cos-1 x r and simplify your answer.

[Q2] (a) Find y I for the function

[Q3] Evaluate the foHowing integrals:-

(a) fln(x 2 + l)dx

"" 2 . A

fLX . -x +4 dx(b) x 3 + 4x .

[Q4]W

f~

a) Discuss the convergence of the improper integral 1 dx .1 X + nx

1

lim (1+ 3x )3lnxb) Find x -7CXl

[Q5] Test the convergence of the following seriesco n3

a) ,,-~?nn=l -

(X) (-lrb) ~ --;~n=(=n =+ 3=)

o

[Q6] Find the interval and radius of convergence of the power series00 {x -IfI~~(1)n=!.J n +

i

[Q7](a) Find the Maclaurin series of the function f (x) = sinh 5x .

(b) Find the vertices, foci, center; and asymptotes of the conic sectionx2-4y2+2x +8y -7=0.

v

Islamic University of GazaDepartment of Math.Summer Semester 16 19/2014

Calculus BFinal ExamTime: 2hours

~~\ Ql Q2 Q3 Q4 Q5 Q6 Q71 Q8 Total

~)I 12 10 18 10 I 14 16 10010 10!

~Jj"J\I I Ii

Solve the following questions:

[Ql] (a) Let f (x) = logx e, x > 1.

(i) Show that f -I (x) exists.

(ii)Find f -1(x ).

(b) Find y I for the function y = (sin -1 x t -(cos-I x r and simplify your answer.