Spring, 2014-2015

EXERCISE 2

1.Differentiate the following functions with respect to (w.r.t.) x:(a)

(b) (c)

(d)

(e) (f) (g)

(h) (i) (j).

(k) (l)

(m)(n)

(o)

(p)

(q)(r)

(s)

(t) (v)

2.Find for the following:

(a)

(b)

(c)

(d)

(e)

(f) .

3. (a) Given that , find , in terms of e, find the value of & at .(b) Given that , show that .4.Find the derivative of

(a)

(b) (c)

(d) .

5.Find the equations of the tangent line and normal to the curve at the point . Sketch the curve, tangent and normal.6. Find the equation of the tangent to the curve at . Sketch the curve and the tangent.

7. Find the equation of the tangent to the curve at the point . Also find the equation of the normal at the same point.

8. Find the equations of the tangent and normal lines to the graph of at thepoint (1,2).

9. Find k if the line is tangent to the curve .

10. At what point(s) the tangent line to the curve is parallel tothex- axis.

11. Show that the triangle that is formed by any tangent line to the graph of , x>0 and

coordinate axes has an area of 2 square units.

12. Find the equations of tangent and normal to the curve .

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