Find all values of a and b that make -a - x, x< -2 /(x) = { Vx + b, bx² + 1, -2 Sx<1 x21 continuous everywhere.

Q: Sketch a continuous function ƒ that is positive over the interval [0, 1) and negative over the…

A: Given that f(x) is posotive over [0,1) and negative over (1,2] And the area bounded by f(x) and…

Q: Compute or show divergence: 1 а. dx 3 Vx+1

A: In this question, the concept of integration is applied. Integration Integration is a method of…

Q: 1. Give an example of a bounded function which is not Riemann integrable over (0,1).

A: According to experts guidelines of bartleby i have solve first question so repost for further…

Q: Find the area under the curve f(x) = 2x* from x = - 3 to x = 2. Area %3D

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Q: Find the average value of f(x) = sin³ x cos³x on the interval [0,1].

A: We need to find average value.

Q: (a) Express the area under the curve y = x 5  from 0 to 2 asa limit.

A: Given

Q: ) Use integration by parts to verify the reduction cosxsin x n-1 Scos" xdx=!

A: Here I=∫cosndx ⇒I=∫cosn-1x×cosx dx using integration by part;

Q: y = - x2 - 6x - 3, y = - x2 - 8x – 13, x = -5, x = -2 are bounded. Determine its area.

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Q: Let f(x) = x sin(2 x). Find its average value for 0sxs/2.

A: Given the query is to find the average value of function over the interval [0,π/2].

Q: RAODUS FIND a of ConuELLENCE foNo AMD INTEiL OF ConvenCENck Of THE (x-3)

A: We have to find radius of convegence and interval of convergence

Q: Illustrate the setting up limits of a double integral?

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Q: Evaluate the integral dx fax √2x-x1

A: Given: I=∫dx2x-x2   As we know the common integral; ∫11-x2dx=sin-1x+C

Q: xlnx at 0<x<1 1-X Show that the function f(x)= is integrable on the interval [0,1]. x = 0 x = 1 at…

A: Given: fx=xlnx1-x,0&lt;x&lt;10,x=0-1,x=1 To prove: f is integrable on 0,1.

Q: integrate f(x) =x^3 * exp(1.33*x) from 1.26 to 2.01 with simpsons 3/8 method use 21 intervals for…

A: Given that, f(x)=x3(e1.33x) , from 1.26 to 2.01 with 21 intervals  To determine The integration…

Q: Find the average value of the function on the indicated interval: 2. f(x) = 3xVx² – 16; x € [4,5] -

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Q: Find F'(x), where F(x)= int. of ((t^2)+1)dt, from sin(3x) to x=-4. Use the 1st rule of the…

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Q: Use integration by parts to prove the reductionformula.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find two z values so that 53% of the middle area is bounded by them.

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Q: Evaluate the integral. 1//3 3earctan(y) dy -V3 1 + y2

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Q: What is the integrable form of et dx? e-e-X

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Q: Q2. Give a counterexample about a bounded function that is not Riemann integrable.

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Q: area bounded by y= 3, x = 2, y = -3 and x = 0 is revolved about the y-axis

A: Given that y=3, x=2, y=-3 and x=0 Find area

Q: f(x) = x^2 − 3x + 2 and the line g(x) = x − 1 over the interval [0,2] .

A: Being bounded means that one can enclose the whole graph between two horizontal lines.

Q: Find the area bounded by the curve y = x² – 6x + 5 and the x-axis from -2 to 2 using %3D Riemann…

A: area bounded by curve using Riemann sum

Q: What is the local linearization of f(x) = arcsin(1+4x) near x = −1/4   arcsin(1+4x) ≈

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Q: 3. Determine the largest interval where j(x) = Vr² – 1 is continuous.

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Q: Find the betwween/bounded by area the Curue u=4y-x² and The line. 4=8-Zx.

A: Sketch the two curves From the graph, we observe that both curves intersect at x = 2 and x = 4.

Q: integral of sqrt(9-x^2)(x)dx. limits are from 0 to 3

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Q: Use integral tables to evaluate. 1 dx; x> 3. 2xV9x -1

A: The following integral: ∫32x9x2-1dx; x&gt;13.

Q: Determine the exact area of the region bound by the graph of f(x) = −x^2 + 5 and the x-axis on…

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Q: Express the limit as a definite integral. 9. Ск lim 2 P → 0k= 1 Axk, where P is a partition of [- 5,…

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Q: -f integration for

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Q: Find F '(x). F(x) = integral of 2/(x+8) dt in interval [x^2,0]

A: Let u=x^2 Then du/dx=2x

Q: Vx - 2 dx

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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: Find the antiderivative of the improper interval xe-x^2 from negative infinity to positive infinity

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Q: Find the area under the curve y = lines x = 1 and x = 5. 3x² + 4x + 1 bounded by the x-axis and the

A: Area under the curve y=3x2+4x+1 bounded by x-axis and x=1 to x=5.

Q: area bounded between y=3x+2 and y=-x^2+2

A: here we have to find the area bounded between the curve y=3x+2......(1) and y=-x2+2x+4.....(2)

Q: The area bounded by the curves y = 1 -x2 and y = - x2 + 2 x + 3 , line x = -1 and x = 1 is

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Q: 6. Find the area bounded by the curves of y = 6x + x² andy = -x² - 2x, and the linex = 5.

A: The equation of the curves are  C1: y = 6x+x2C2: y = -x2-2xC3: x = 5 To evaluate: The area of the…

Q: Find the area of a triangle bounded by the y axis, the line 2 f(x) = 6 - x, and the line…

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Q: Find the absolute makimum/minimum values of the function fCx)= x6-x) over the intenval 1Ex<5

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Q: y = Vx - x² - re sen /x

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Q: : Determine the area of bounded by y = 2x-1, and y = 4x-2 on interval [1,4].

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Q: The area of the region bounded by the function f(x) = + 3, lines x = −2, x = 2 and the x — axis is…

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Q: find the area between the curves: f(x) = x2  + 1,   g(x) = 3 - x   on the interval [0,3]

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Q: sketch the described regions of integration. -1 ≤ x ≤2, x - 1≤ y ≤ x2

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Q: Every function which is riemann integrable on [a, b] is continuous.true or false

A: To check if every function which is riemann integrable on [a, b] is continuous or not.

Q: Find the area (sq. units) covered by the line y = -Gx+ 3) from x1 = -8 to x2 = 0.

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

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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.