Between two consecutive real roots of f(x) =0 there exists___________of f’ (x) =0.
at least one real root
at least one real root or even number of real roots
at least one or an odd number of real roots
No real root
Between two consecutive real roots of f’(x) =0 lies _________of f(x) =0
At most real root
at most one or odd number of real roots
at most one or even number of real roots
No l root
?[f(x)g(x)] equals
f(x+h)?g(x) - g(x+h)?f(x)
f(x)?g(x)+ g(x)? f(x)
f(x+h)?g(x)+ g(x)? f(x)
f(x+h)?g(x)- g(x)? f(x)
Which of the following is true?
?=E –I/2 + EI/2
d=EI/2 ?
?=E –I/2 ?
None of the above
Let ?f(x) =f(x+h)-f(x) for a constant K, ?k equals_________?
1
0
f(k)-f(0)
f(x+k)-f(x)
Picard’s method in numerical solution of differential equation is based on
Forward interpolation
Backward interpolation
Converging sequence of successive approximations
Successive integration
The Newton-Raphson method is applied to find a root of the equation x2-2=0. if the iterations are started from -1 then the iteration will be ?
Converge to -1
Converge to v2
Converge to -v2
Not converge
In Euler’s method to solve y’(t)=f(t),y(0)=0, i th step size h the first four iterations will yield the following values of y.
0,hf(0),h[f(0)+f(h)+f(2h)]
0,0,h2f(0) and 2h2 [f(0)+f(h)+f(2h)]
0,0,h2f(0) and 3h2 f(1)
None of the above
What are the different types of interpolation?
Forward differences
Backward differences
Central differences
All of the above
In numerical integration in the trapezoidal rule what is the value of n?
n=2
n=3
n=4
None of the above