Basic Mathematics 2077

Section A

Long Answer Questions.

Attempt any two questions.        (2x10=20)

1.  (i) What is even and odd function? Give example of each and write their symmetricity.                                                                                                         (1+1+1+1+1+1)

    (ii) Find the domain and range of the following functions.

                    (2)

                  (2)

2. Find the Tayllor's series generated by  at a=2 where it anywhere, does the series converges to .        (10)

3.  (i) Sketch the graph of the function f(x)=x². Shifted vertically up to 1 and -2 units and horizontally up to 3 and -2 units.

    (ii) Find the  algebraically of the following functions.

            a)         (2.5)

            b)     (2.5)

Section B

Short Answer Questions.

Attempt any eight questions.        (8x5=40)

4.  Find the initial value problem in

5. Determine the convergence or divergence of the series

6. Show that  has a continuous extension to x=2.

7. Evaluate the

        (i)         (2.5)

        (ii)         (2.5)

8. Find the derivatives of the function  at  in the direction of .

9. Integrate the following

10. Find the area of the surface generated by revolving the curve  , about x-axis.

11. Determine the concavity and find the inflection point of the function

        f(x)=x³-3x²+2

12. Find 

        (i) Y = 2u³, u = 8x - 1                    (2.5)

        (ii) Y = sinu, u = x - xcosx              (2.5)