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how many structural isomer of amine are possible with molecular formula C4H11N
In Progress...
Suppose there are initially 2,200 bacteria in a culture and the number of bacteria triple each hour, the number of bacteria after t hours can be found using the formula y = 2200(3)t. How long will it take the culture to grow to 60,000 bacteria?

In Progress...
i) Calculate the third-degree Taylor polynomial about 0 x0 = for 2/1
f (x) = 1( + x) .
ii) Use the polynomial in part (i) to approximate 1.1 and find a bound for the
error involved.
iii) Use the polynomial in part (i) to approximate ∫
+
1.0
0
/1 2
1( x) dx .
In Progress...
Using the following table of values, find approximately by Simpson’s rule, the arc
length of the graph
x
y
1
= between the points )1,1( and 





5
1
,5
x 1 2 3 4 5
4
4
1
x
+ x
1.414 1.031 1.007 1.002 1.001
In Progress...
Show that x x
x
u c e c e
α −α
= 1 + 2
is a solution of the difference equation
2 cosh 0 ux+1 − ux α + ux−1 =
In Progress...
Use modified Euler’s method to find the approximate solution of IVP
1 y′ = 2xy, y )1( = at x = 5.1 with h = 1.0
If the exact solution is 1
2
( )

=
x
y x e , find the error.
In Progress...
Compute the values of

+
=
1
0
2
1
1
x
dx
by using the trapezoidal rule with 125 h = ,5.0 25.0 , .0 . Improve this value by using
the Romberg’s method. Compare your result with the true value.
In Progress...
Using the classical R-K method of ) (
4 O h calculate approximate solution of the IVP,
y′ = 1− x + 4y, y )0( = 1 at x = 6.0 , taking h = 1.0 and 2.0 . Use extrapolation
technique to improve the accuracy.
In Progress...
A table of values is to be constructed for the function ) f (x given by
x
f x
+
=
1
1
( ) in
the interval ]4,1[ with equal step length. Determine the spacing h such that
quadratic interpolation gives result with accuracy 6
1 10−
× .
In Progress...
Show that
2
1 1
2
2 2 δ
+ µ δ = + where µ and δ are the average and central
differences operators, respectively
In Progress...
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