1. Determine the following and simplify if possible. +fixcosh 2 X 1.1 sink 2xe sin. x 1.2 y = by...

Question

1. Determine the following and simplify if possible. +fix
cosh 2 X 1.1 sink 2x
e sin. x 1.2 y = by using logarithmic differentiation. + x2 1.3 x3y + xy2= x 2. A particle moves along the path y = x –0,5x2 such that dx— =10 . dt
Find the value of when x = 5. dt
x\ 2z 2z 3. If z = arctan , show that —ax2+ = O.
d2 y 4. If y = cost and x = e2( sin 2t find —dx2 at t =0 5. The heat generated in a resistance weld is given by H =1d2Rt,where k is a constant, I is the current between the electrodes and t is the time for which current flows. H must not vary with more than 5% if the weld is to remain good. It is possible to control t to within 0,5% and R to within 2,4%. Estimate the maximum possible variation in current, I, if the weld is to retain its quality XXXXXXXXXXWrite down the first non-zero term in the Maclaurin series expansion of f (x) = .en sec x. (4) TOTAL: 40
'Sr
15
r49

005_h2xa5o-vsnbln3b.pdf

David · Accepted Answer

1. (y’ denotes dy/dx) 
1.1 y=
x
x
2sin
cosh 2
=
x
ee xx
2sin
1
)
2
( 2

=
x
ee xx
2sin4
222  
 
x
eexeex
y
xxxx
2sin16
)2(2cos8)22(2sin4
'
2
2222 


                 (ans)
1.2 
21
sin
x
xe
y
x

  
2
)1ln(
sinlnln
2x
xxy

  
Differentiating, we have 
21sin
cos
1
'
x
x
x
x
y
y

             
)
1
cot1(
1
sin
'
22 x
x
x
x
xe
y
x



                       (ans)
1.3 xxyyx  23  
Differentiating this whole equation w.r.t x,

1. Determine the following and simplify if possible. +fix cosh 2 X 1.1 sink 2x e sin. x 1.2 y = by using logarithmic differentiation. + x2 1.3 x3y + xy2= x 2. A particle moves along the path y = x...

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