Tag: the need for approximation

Quizzes (0) Questions (56)

Questions Related to the need for approximation

Multiple choice maths the trapezium rule approximation errors and approximations the need for approximation

The positive root of ${x}^{2}-98.8=0$ after first approximation by Newton Raphson method assuming initial approximation to the root is $14$ is

  1. $9.821$
  2. $9.814$
  3. $9.715$
  4. $9.915$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Here ${x} _{0}=14, f(x)={x}^{2}-78.8$
and $f'(x)=2x$
$\therefore$ ${x} _{1}={x} _{0}-\cfrac{f({x} _{0}}{f'({x} _{0})}$
$=14-\cfrac { { \left( 14 \right)  }^{ 2 }-\left( 78.8 \right)  }{ 2\times 14 } =9.814$

Multiple choice maths the trapezium rule approximation errors and approximations the need for approximation

State the following statement is True or False

According to the Newton-Raphson's method the approximate root of the equation $f(x) = 0$ is $x _{n}$ then be $x _{n} = x _{n + 1} - \dfrac {f(x)}{f'(x _{n})}$.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
If $x _n$ is the approximate root of $f(x)=0$ then the value of $x _n$ given by Iterative eqn. for Newton-Raphson method is 
    ${ x } _{ n+1 }= { x } _{ n } - \dfrac { f({ x } _{ n }) }{ f' ({ x } _{ n }) } $, where $f'(x _n)$ is derivative of $f$ at $x _n$

$\therefore $ The given statement is FALSE.
Multiple choice maths the trapezium rule approximation errors and approximations the need for approximation

Find the approximate error in the volume of a cube with edge $x$ cm, when the edge is increased by $2\%$

  1. $4\%$
  2. $2\%$
  3. $6\%$
  4. $8\%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

in a mutiplication while multiplying we have to add the percentage errors 


so if the edge of the cube is $x$cm then the volume will be ${ x }^{ 3 }$

but for errors we have to add the percentage 

therefore the total error  percentage now becomes $6\%$

therefore the error is increased by $4\%$