MTH603 Quiz 1 Solution and Discussion

• Logarithmic Function

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.

• Exponential Function

In mathematics, an exponential function is a function of the form. where b is a positive real number, and in which the argument x occurs as an exponent. For real numbers c and d, a function of the form is also an exponential function, as it can be rewritten as.

• Trigonometric Function

In mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

• In Newton-Cotes formula for finding the definite integral of a tabular function, which of the following is taken as an approximate function then find the desired integral? MTH603

In numerical analysis, Simpson’s method is a method for numerical integration, the numerical approximation of definite integrals. … Simpson’s rule also corresponds to the three-point Newton-Cotes quadrature rule

• Series acceleration method

In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series. Techniques for series acceleration are often applied in numerical analysis, where they are used to improve the speed of numerical integration.

• Sequence acceleration method

In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series. Techniques for series acceleration are often applied in numerical analysis, where they are used to improve the speed of numerical integration.

• δ = E 1/2 - E 1/2

• In Simpson’s 1/3 rule, the global error is of ……………… MTH603

O(h2)

O(h3)

O(h4) Page=171

Non of the given choices

• Richardson extrapolation is method also known as ………… MTH603
Sequence acceleration method
Series acceleration method

• 3rd

• In Newton-Cotes formula for finding the definite integral of a tabular function, which of the following is taken as an approximate function then find the desired integral? MTH603

Trigonometric Function

Exponential Function

Logarithmic Function

Polynomial Function Page=166

• While using the Composite Trapezoidal form for integrating y = f(x) in [0,10] which is subdivided in equally spaced interval of width ‘h =2’, then which of the following is the area of associated trapezoidal strip over subinterval:[2,4] ? MTH603
(y2 + y4)/2
(y2 + y4)
(y2 - y4)/2
(y2 - y4)

• For a function ‘f(x) = x’, with a step size of ‘h=0.01’, which of the following gives the 1st derivative at x =1 by using two point formula? MTH603

Y’=(x)=1+Some truncation Error

Y’=(x)=1.01+Some truncation Error

Y’=(x)=.0.1+Some truncation Error

Y’=(x)=0.1+Some truncation Error

1

1

7

7

4

3

3

4
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