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Sma2161:Mathematics Ii Question Paper

Sma2161:Mathematics Ii

Course:Bachelor Of Horticulture

Institution: Meru University Of Science And Technology question papers

Exam Year:2014

QUESTION ONE – (30 MARKS)
(a) Evaluate the following
(i)
9
6
3
lim
2
2 ?
?? ?? x xx
x
(3 Marks)
(ii)
734 5lim 2 2 ???? xx x
x
(3 Marks)
(b) Find the derivatives of the following functions (i) ? ? 1 2 1 4 2 ? ? ? ? ? ? ? ?? x xy (2 Marks)
2
(ii)
12
3 ?
?
x x y (2 Marks) (iii) ? ?3 223 xxy ?? (2 Marks)
(c) Find ? ? xf / from the first principles given that ? ? x xf sin ? (4 Marks)
(d) Find
dx dy
if 3 32 4x yy ? ? (3 Marks)
(e) Find and classify the turning points of the curve represented by the function.
12492 23 ? ??? x xxy (4 Marks) (f) Evaluate the integral dx x? 5cos (4 Marks) (g) Find the function f that satisfies ? ? ? ? 6 5 1,532/ ? ??? f andxxxf (3 Marks)
QUESTION TWO – (20 MARKS)
(a) Given that ?? ?? = 5?? - 3 and ? ?
5 2
5 ?? xxg . Find
(i) ? ? xf 1? (2 Marks)
(ii) ? ? xfg 1?? (2 Marks)
(b) Find
dx dy
if;
(i) x xx e xeexy 2 22 ? ?? (4 Marks)
(ii) ? ? ? ? ? ? ? ? ? ? ? 42 2 ln 2 2 x x y (3 Marks)
(iii) x xy cos 56 ?? (2 Marks)
(c) Evaluate
? ? h xhx
h
22 33
0 lim ? ? ?
(3 Marks)
3
(d) Air is being pumped into a spherical balloon so that its volume increases at a rate of 100????3/??. How fast is the radius of the balloon increasing when the diameter is 50cm? (4 Marks)
QUESTION THREE – (20 MARKS)
(a) Evaluate the definite integrals. (i) ? ?? ?dx xx 1 33 1 1 ??? ? (3 Marks)
(ii) ? ?dx xx? ? ?2 2 cos3sin ? ?
(3 Marks)
(b) Use integration by parts to find: dtet t? (4 Marks)
(c) (i) Express
32 35 2 ? ? ? xx x
in partial fractions. (4 Marks)
(ii) Hence evaluate dx xx x? ? ? ? 32 35 2 (2 Marks) (d) The region bounded by the graphs of x y ? and 2 2 xy ?? the x-axis is revolved about the x-axis. What is the resulting volume? (4 Marks)
QUESTION FOUR – (20 MARKS)
(a) Find ? ? dx x x? ? 53 2 1 3
by using the substitution ?? = ??3 - 1 (3 Marks)
(b) A farmer has 100m of wire-mesh to fence a rectangular enclosure. What is the greatest area he can enclose with the wire-mesh? (4 Marks)
(c) If t ex t ? ? and t ey t 2 2 ?? . Find
dt dy
(5 Marks)
(d) Supplies are dropped from a helicopter and the distance fallen in a time t seconds is given by 2 9.4 ts ? . Determine the velocity and acceleration of the supplies after it has fallen for 2 seconds. (4 Marks)
4
(e) Find
dx dy
given that x xy 5 cos3sin 4 2? (4 Marks)

Sma2161:Mathematics Ii Question Paper

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