Numerical Analysis 1

If y(x)=e^x then y(0) and y(1) are

• 1, 2.7183

• 2,3

• 1,2

• 2,4

In numerical integration the width of the sub intervals is given by

• $h=\frac{x_n-x_0}{n}$

• $h=\frac{x_n+x_0}{n}$

• $h=\frac{x_0-x_n}{n}$

• none of thesse

In Trapezoidal rule, for the interval (0,1) if h=0.25 then the value of n is_________

• 1

• 2

• 3

• 4

    By Trapezoidal rule,

 $\int_{x_0}^{x_n}ydx=---$  

•  $\frac{h}{2}\left(y_0+2\left(y_1+y_2+...+y_{n-1}\right)+y_{n_{ }}\right)$  

•  $\frac{h}{2}\left(y_0-2\left(y_1+y_2+...+y_{n-1}\right)+y_{n_{ }}\right)$  

•  $\frac{h}{2}\left(y_0+2\left(y_1+y_2+...+y_{n-1}\right)-y_{n_{ }}\right)$  

•  $\frac{h}{3}\left(y_0+2\left(y_1+y_2+...+y_{n-1}\right)+y_{n_{ }}\right)$  

Simpson’s 3/8 rule is applicable only when n is a multiple of 3.

• True

• False

Simpson’s 1/3 rule is applicable for five ordinates.

• True

• False

Simpson’s 3/8 rule is applicable for nine ordinates.

• True

• False

Simpson’s 1/3 formula is not a closed formula.

• True

• False

If y(x)=sinx,then  $y\left(\frac{\pi}{2}\right)=$  

• 1

• -1

• 0

• 1/2

The process of computing the value of a function inside the given range is called interpolation.

• True

• False