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What are vectors that are not parrallel to the same line,called.
scalar
collinear vectors
non-collinear vectors
vectors
scalar
collinear vectors
non-collinear vectors
vectors
A dot product is said to be distributive,if
..
m.u=u.m
m(u.v)=v(m.v)
u.(v+w)=(u.v+u.w)
m=u
m.u=u.m
m(u.v)=v(m.v)
u.(v+w)=(u.v+u.w)
m=u
Tf u.v=v.u,what does the law conotes;
associative
commutative
distributive
scalar
associative
commutative
distributive
scalar
The sum of a vector and the negative of another vector could be written as
w+w
w+(-w)
w
None of the above
w+w
w+(-w)
w
None of the above
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 .
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 .
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
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
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 =
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 =
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.
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.
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.
∫
+
=
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.
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.
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.
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#339914 on Dec 2023
#339914 on Dec 2023