Computational Methods_BEYOND

Taylor series becomes more accurate when the function we are approximating becomes more like a ______________ line over the interval of interest.

The total __________ is the summation of the truncation and round-off errors.

_____________________________expansion can be used to derive numerical estimates of higher derivatives.

A condition number can be defined as the ratio of the __________errors.

• variation

• relative

• distortion

• discrepancy

The method of ___________ is used to solve non-linear equations in computational methods.

• Subtraction

• Bisection

• Multiplication

• Addition

The remainder term in Taylor's theorem helps in estimating the error in approximation.

• False

• True

Which of the following statements about the Maclaurin series is true?

• It can only approximate simple functions

• It is limited to specific types of functions

• It can be used to approximate functions around x=0

• None of the above

A computation is numerically ____________if the uncertainty of the input values is grossly magnified by the numerical method.

• Accurate

• Stable

• Unstable

• Precise

The nth-order Taylor series expansion will be exact for trigonometric functions.

• True

• False

Taylor series is used to estimate numerical errors by approximating a function as an infinite sum of terms.

• TRUE

• FALSE