MTH603 Quiz 1 Solution and Discussion

@zareen said in 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.
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@zareen said in MTH603 Quiz 1 Solution and Discussion:
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.

@zareen said in MTH603 Quiz 1 Solution and Discussion:
Trigonometric Function
In mathematics, the trigonometric functions are real functions which relate an angle of a rightangled 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.

@zareen said in MTH603 Quiz 1 Solution and Discussion:
In NewtonCotes 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 threepoint NewtonCotes quadrature rule

@zareen said in MTH603 Quiz 1 Solution and Discussion:
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.
link text 
@zareen said in MTH603 Quiz 1 Solution and Discussion:
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 NewtonCotes 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
