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Calculus Question Paper

Calculus

Course:Certificate In Bridging Mathematics

Institution: Kca University question papers

Exam Year:2012

1
UNIVERSITY EXAMINATIONS: 2011/2012
EXAMINATION FOR THE CERTIFICATE IN BRIDGING MATHEMATICS
MAT 103 CALCULUS
DATE: APRIL 2012 TIME: 1½ HOURS
INSTRUCTIONS: Answer Question One and Any other Two Questions
QUESTION ONE
a) Given that y=2x2-5x+7 use the first principle of differentiation to find the derivative of y with
respect to x. (5 Marks)
b) Use product rule to differentiate the following functions with respect to x.
Y=x cos x (3 Marks)
c) Evaluate the following limit.
4
2 12
4 -
-
? x
Lim x x (4 Marks)
d) Use power rule to get the derivative of : y = 2x3 - 3x + 6 (2 Marks)
e) Integrate the following function; ?(x3 - 2)63x2dx (6 Marks)
f) Find the equation of the tangent line to the equation y=3x2-5x+6 at (1,4) (5Marks)
g) Find the integral of; ?sin(4x)dx. (5 Marks)
QUESTION TWO
a) Using product rule find the first derivative of the following functions;
i) Y=(2x2 – 2x)(x+4) (5 Marks)
b) Use chain rule to differentiate y=(3x2+2)6 (5 Marks)
c) Determine the gradient of
3 1
3 2
+
=
X
y X at the point p (2,1) (5 Marks)
2
QUESTION THREE
a) Find the derivative of .y = e4x sin 3x (7 Marks)
b) Find the normal line to the equation y=3x-x2 at the point (3,0). (8 Marks)
QUESTION FOUR
a) Evaluate the following integrals.
i) ? + 4
0
x2 9xdx (5 Marks)
ii) (5 Marks)
b) Given the point y=x3-12x. Determine the nature of the turning points (5 Marks)
QUESTION FIVE
a) Given the functionx3y2=x, find at the point (1,2) using implicit differentiation. (8 Marks)
b) Determine the first derivative with respect to x for the following function.
y = ln 4x2 - 5x (7 Marks)

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