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Ccs 109:Basic Calculus Question Paper

Ccs 109:Basic Calculus

Course:Bachelor Of Science In Computer Science

Institution: Maseno University question papers

Exam Year:2014

PART A:ANSWER ALL QUESTIONS( 30 MARKS)
Question one(30 marks)
a)Differentiate from first principles f(x)=x2 and determine the value of the gradient of the curve at x=2.(4mks)
b)State the Chain rule and use it to evaluate the first derivatives of the following functions
i)y=ln(3x-4). (4mks)
ii)y=-2e(1-3x). (4mks)
c)Use the product rule to find the differential coefficient of
y=sin(t) cos(3t). (4mks)
d)Evaluate the definite integral 0?/6[sin(3x+2)dx]. (4mks)
e)If y=f(x)=2x5-4x3+3x-5 find y. (4mks)
f)Differentiate from first principles f(x)=x2 and determine the value of the gradient of the curve at x=2. (5mks)
g)Supplies are dropped from a helicopter and the distance fallen in time t seconds is given by x=1/2gt2,where g=9.8m/s2.Determine the velocity and acceleration of the supplies after it has fallen for 2 seconds. (5mks)

PART B:ANSWER ONLY TWO QUESTIONS (20 MARKS EACH)
Question Two(20 marks)
a)The velocity of a spring is found to be V=6 sin(3?t).Assuming that the spring is perfect,so that v=(1/k)(dF/dT),where k is the spring constant (known to be 0.5),v the velocity,and F the force operating on the spring,find the force,given that it is 0N initially.(8mks)
b)A ball is thrown in the air so that the height of the ball is found to be s=3t - 5t2.Find;(12mks)
i)The ball's initial velocity when first thrown in to the air;
ii)the time when it returns to the ground;
iii)its final velocity as it hits the ground.

Question Three(20 marks)
a)Find the derivatives of system described by the function y=(4sin 5x)/(5x4) (10mks)
b)Find the partial fractions of (5x+2)/(3x2+x-4) and hence evaluate the integral of
(5x+2)/(3x2+x-4). (10mks)

Question Four(20 marks)
a)Use integration by parts formula and use it to find the integral of
x{x/(x2+1)}dx. (10mks)
b)Find the area enclosed between the x axis and the curve y=x3+2x+x+1 between x=-2 and x=2. (10mks)

Question Five(20 marks)
a)The potential due to a point charge Q at a position r from the charge is given by V=Q/(4?£0r) where £,the permittivity of free space, =8.85 X 10-12 Fm-1 and ?=3.14.Given that Q=1 C,find the electric field strength at a distance of 5m using E=-dV/dr. (10mks)
b)Determine the rate of charge of voltage ,given v=5t sin 2t volts when t=0.2s. (10mks)

Ccs 109:Basic Calculus Question Paper

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