(6) Construct a non-negative finitely additive function lo on P (N) that is not a measure. Hint: define lo separately for finite and for infinite sets.

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A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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A: If derivative greater than zero then increasing

Q: The graph of the derivative f' of a function f is shown. 8 10 2 14 16 18 (a) On what interval is f…

A: Vvvvv EU I up vhuh

Q: The function fx) =x² - 6x + 1 has an absolute minimumon (0,5] at x = OA -3 OB 3 OC5 OD.O QUESTION 29…

A: To find the value of x at which the function attains absolute maxima and minima.

Q: d. On what interval(s) of x is ƒ(x) decreasing? Preview e. On what interval(s) of x is f concave up?…

A: solution:-(d) f(x) is decreasing in the interval x∈-0.5, ∞(e)f(x) is concave up in the interval =DNE

Q: For what value of k will the function f be continuous on (-∞, 0)? { x2 – 16 if x + -4 f(x) = x + 4 k…

A: We have to find

Q: For what value of the constant c is the function f continuous on (-0, 00)? C =

A:

Q: On what domain is the function f(x) = – 4+ V3x – 6 continuous? %3D

A: The function is a square root function and hence, the function is continuous in the domain.

Q: Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ≈ T₁(x) when x lies in…

A:

Q: Find the absolute Extrema of given Function, on given interval and state where those values occur.…

A:

Q: (b)(is) Verify that the function satisfies the hypotheses of Rolle's Theorem on the given interval.…

A: Explanation of the answer is as follows

Q: 54. Is the function given by SEx + 4, for x s 3, 2x – 1, for x > 3, g(x) continuous at x = 3? Why or…

A: The given function is;  g(x)=13x+4for x≤32x-1, x>3 we have to check the given function is…

Q: On what intervals are the following functions continuous? k(x) = x-1/6

A:

Q: or each of the following statements, determine if they are true or false. In either situation,…

A: stgsment is false5

Q: On which interval is the function )--- increasing? A I1

A: f(x)=-x3-x2⇒f'(x)=-3x2-2x

Q: Consider the following function: - 4 if x 3 Find the values of a and b that make f continuous…

A: The function is continuous every where, if it is continuous at each point in the domain. The…

Q: Let f(x) be defined by f(x) = x − 2 ln(x), for x > 0 Part a: On what intervals (if any) is this…

A: For increasing f'(x)>0

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A:

Q: Let f(x) = x³e-3=. (a) On what exact interval(s) is ƒ increasing? decreasing? Make it clear which…

A: Consider the given function  fx=x3e-3x

Q: Find the absolute extreme values of the function on the given closed interval. 1 (x) = 10 + 27 x – x…

A:

Q: x+x², 0<x <=

A: Continuity: The function f is continuous at some point c of its domain if the limit of f(x), as x…

Q: х2+1 h(x): %3D х-5

A: A rational function is continuous for all real numbers except at which the denominator is zero.…

Q: Find the area between the graphs of the given functions f(x) =x+2, and g(x) =x' -4

A:

Q: Determine the intervals on which the function shown, is concave up or concave down.

A: Solution- We have to find the g(x) to evaluate the intervals where function is concave up or down.…

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

A: Given,          fx=1x+lnx ; 0.4≤x≤9

Q: Answer the following questions for the function f(x) = xvx? + 9 defined on the interval [-6, 4]. a.)…

A:

Q: Suppose that the function f(x) is continuous everywhere. Suppose further that the points (x, y),…

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Q: 3. Find the value of k that makes each function continuous over the given interval.

A: If function are continuous then both the side are equal

Q: Given the function f(x) =4x3 – 39x²+ 90x+ 2, which of the following describes its absolute extrema…

A:

Q: Find the absolute extrema of the function f(x) = x3 − 3x2 − 24x + 5 on [−3, 6], if they exist as…

A: We have to solve given problem:

Q: For what value of k is the following a continuous function?

A: Function is continuous if   limx→2-f(x)=limx→2+f(x)=limx→2f(x)

Q: Q3: determine whether following function are continuous ore not 4 X# 2 f(x): x-2 4 X = 2

A: To determine whether the below function is continuous or not. fx=x2−4x−2,       x≠24,…

Q: from x = 1 to x = 4 2

A:

Q: Find the open intervals on which the function is increasing or decreasing         h(x) = √x(x − 3),…

A: For a critical point, we solve h'(x)=0

Q: Consider the function f(x)=−2x3+36x2−162x+9f(x)=−2x3+36x2−162x+9. For this function there are three…

A:

Q: For what values of k will the function below be continuous for all x? x³, xsk h(x) = x², x > k 1 and…

A: The function is said to be continuous at x=k if limx→k-f(x)=limx→k+f(x)=f(k).

Q: There is an entire function whose value on n E N is (n – 1)!. Select one: True False

A: The objective is to determine whether the statements is true or false. There does not exist an…

Q: Find the value of "k" , given that the following function f(x) is continuous at x = 3 OL + 8, f(x) =…

A:

Q: Answer the following questions about the function below. y = 4x2 – 8x + 9 on the interval [-1,3]…

A: Given function, f(x)=4x2-8x+9 on the interval [-1,3] To explain why the function satisfies all three…

Q: ) On what interval(s) is f increasing ? y= f{(x)} ) At what value(s) of x, if any, does f have a…

A: graph  Given graph of f'(x) determine properties of f(x) f'=0 ⇒critical points of f  f'&gt;0 ⇒f…

Q: Consider the graph of f below. LA f(x) a b Does the function appear to satisfy the hypotheses of the…

A: We are given graph of the function. we have to check if it follows Mean Value Theorem.

Q: 18. Consider the function f (x) 5e2r. On what interval(s) is f (x) %3D increasing? On what…

A:

Q: Find a value for the constant k, if possible, that kæ? if x 2 Is the function f(x) = 1 continuous…

A:

Q: 3. Find the absolute extrema of the following function on the indicated interval. f(x) = x3 – 3x on…

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Q: Find a point e satisfying the conclusion of the MVT for the following function and interval: f(x) =…

A:

Q: Is the following function continuous or discontinuous? If disco where? Justify all answers. a. f(x)…

A: As per our guidelines we are supposed to solve only first three subparts of the problem. For the…

Q: 7. Find the intervals on which the function is continuous, J (X) = +3)2+6

A:

Q: 1 g(x) = 1 +3 x E [1,5]

A:

Q: 1. Find the absolute extrema for the following function over the given interval: f(#) = * - + 2 +2…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.