Purchase Solution

# Calculus : Partitions and Riemann Integral

Not what you're looking for?

Let f be the function:
F(x)
1/4 x=o,
x 0<x<1
3/4 x=1

Using standard partition Pn (0,1) where n greater or equal to 4

L(f, Pn) = 2n(squared) -3n+4 all divided by 4n(squared)

U(f,Pn) = 2n(squared) +3n+4 all divided by 4n(squared)

and deduce that f is intergrable on (0,1) and evaluate
(intergral sign with 1 at top and 0 at bottom) of f

##### Solution Summary

A function is proven to be integrable over a given range.

##### Solution Preview

Since,
dL/dn =0=> n = 8/3 and d^2L/dn^2 = +ve
=> L has minima at n =8/3 < 4 => increasing fn for n>= 4
therefore,
suprema(L) = lim(n->infinity) L = lim(n->inf) {2/4 -3/4n +4/4n^2}
=> ...

Solution provided by:
###### Education
• MSc , Pune University, India
• PhD (IP), Pune University, India
###### Recent Feedback
• " In question 2, you incorrectly add in the \$3.00 dividend that was just paid to determine the value of the stock price using the dividend discount model. In question 4 response, it should have also been recognized that dividend discount models are not useful if any of the parameters used in the model are inaccurate. "
• "feedback: fail to recognize the operating cash flow will not begin until the end of year 3."
• "Great thanks"
• "Perfect solution..thank you"

##### Free BrainMass Quizzes

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Probability Quiz

Some questions on probability

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts