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2 C 22091

el x

dx.
xe

Find |

2
Evaluate | |x| dx.
-1
Find the area of the region between the graphs of y = e* and y = x and the vertical lines
x=Oandx=1.
Find the work done by the force F(x) = 3x? + x in moving a particle along the x-axis from
x=2tox=4.
(10 x 3 = 30 marks)
Section B
Answer at least five questions.
Each question carries 6 marks.

All questions can be attended.
Overall Ceiling 30.

Fi ‏و ے‎ 1
ind lim x*sin—.
x30 x

Let f(x) =2x°+x(a) Find f'(x). (b) What is the slope of the tangent line to the graph of
f at (2, 18) ; (c) How fast is f changing when x = 2.

Find the relative extrema of f(x) =x° —3x? —24x +32 using second derivative test.

Let fix) = x° —x for xin - 1, 11:

(a) Show that f satisfies the hypothesis of Rolle’s theorem on [- 1, 1].

(b) Find the numbers c in (— 1, 1) such that f’(c)=0 by Roll’s theorem.

(a) In a test run of a maglev along a straight elevated monorail track, data obtained from
reading its speedometer indicated that the velocity of the maglev at time ¢ can be
described by the velocity function v(¢t)= 8t,0Assume that the maglevy is initially located at the origin of a co-ordinate line.

dx
1-sinx

(b) Find |

(a) State fundamental theorem of Calculus.

द |>
(0) Find ral 3 by using the above theorem and by performing the integration and

differentiation.

199957