Every function which is Riemann 3/3 integrable on [a,b] is continuous. True False

Q: Let f'be continuous on [a, b], a>0, and differentiable on (a, b). Prove that there exists c = (a, b)…

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Q: Theorem 11. Let f be a continuous function on R such that f(x+y)-f(x)+fv) vx, yER. Show that f(x)3cx…

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Q: On what interval is In(x² + 1) concave up? くxく

A: This question is about concavity of a function

Q: b) Give an example of a function g: R →R that is continuous at some xE R, but not differentiable at…

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Q: If f : a, b] → Ris differentiable at a point c E (a, b), then f is continuous at c. True False

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Q: → R be a function defined by 3x² + x+5 f(x) = not continuous at x = = 0.

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Q: 6. Show that (an)neN C R is bounded if and only if lim supn→∞ an < +∞o.

A: To Prove:  ann is bounded sequence if and only if limsupan&lt;+∞.

Q: True/False; f (x) =; 1 is continuous on 2х —1 A) False B) True If f(-3)=6, f(2)= and f is continuous…

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Q: Is a function Continuous ?why? integrable anod

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Q: Question 3 If f is integrable on the interval [3, 9], then Lf (x)dx = [,'f (x)dx a) True b) False

A: Given query is to find the statement is true or false.

Q: Every function which is Riemann 0/3 integrable on [a,b] is continuous. * True O False

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Q: Suppose that f is differentiable on [a, b]. Prove that if f'(a)f'(b)< 0 then there exists a point c…

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Q: If f : [0, 3] → R is continuous not constant, then its range be a closed, bounded interval?

A: Yes true.

Q: f(x)=xmodx for all x  in R. Discuss the derivability of f(x) at x=0

A: Given:fx=xxwe have to find derivability of fx at x=0

Q: Is the function f(x) = ( 1, x not equal 1)             ( 0, x equal 1) integrable over the interval…

A: Here, we will show that the given function is integrable. Let us take a point c ∈ (0,1).

Q: Only one option can be true

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Q: Q\ Use appropriate functions to guarantee that (). x sin if x # 0 h(x) = 0, if x = 0 is continuous…

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Q: State true or false with brief justification   If T:X----->Y is continuous, linear and open, then…

A: Given statement is If T:X→Y is continuous, linear and open, then T is surjective.

Q: Make sure you do your best to answer all three parts. Suppose f(x) and F(x) are continuous functions…

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.