7. Find a formula for RN for f on [2, 5] and compute f(x) dx by taking the limit.

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Q: 1. Show that for all f e L'(R) lim dr = 0. %3D

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A: Yes, the sequence is given in step 2.

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A: Given

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A: In this we use the limit  definition of definite integral

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Q: 3 B Consider the following function, z= x -2xyty't yn Lind the alues of ag Ddz,z,when redgyel dy 6.

A: Given : z = x2 -2xy + y3 + yw

Q: has a limit at xo + 0. If Q2. Let f:R → R be a function such that f(x) x sin f is defined at xo,…

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Q: 1. Find grad f for the given function below. Ax, y, z) = 5xy + 3yz – 4zx

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Q: Given Rn 4 + 1 4( 4+ i- , express the limit as n → ∞ as a n n n definite integral, that is provide…

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Q: 1. Apply the Parseval's identity to the function f (x) = x, –n < x < n

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Q: for |x| > 1, 2x2 fx,(x) = 0, %3D otherwise. Let L = lim P(max{X1,..., X,} < n log(v5)). Determine…

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A: Given, limk→∞1+110k10k    We have to find the value of the above limit.

Q: Q2. Let f:R→ R be a function such that f(x) = x sin (-) has a limit at xo + 0. If f is defined at xo…

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Q: What is the limit of (In(e+h)-1)/ h at h=0?

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Q: Given that for each a E (0, 1) lim t "(1 – t)"dt exists. Let, this limit be g(a). In addition, it is…

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Q: Find the Wronskian for the set of functions.{ex, e−x}

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Q: Please see picture

A: Introduction:Here, MX (t) denotes the moment generating function (mgf) of the random variable X;…

Q: 3. Convert the limit below into a definite integral and then evaluate it using FTC. 3\²3 1+ n)+2(1+…

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Q: O The limit function of h. )= n'Sinx is ?

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Q: (E) f is defined at xo , where the value of 8 exactly is Q2. Let f:R → R be a function such that…

A: Q2. It is given that,f(x)=xsin(1x) has a limit at x0 not equal to 0.

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Q: Which of the following correctly expresses the limit lim as a definite n00 n5 integral? 1 A. 1 В. dx…

A: Solution is given as below:

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Q: 5. Consider the function S 2r – 1, si x < 2 f(x) = 6-x, si x 2 2. The Limit x 2 f(x) is:

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Q: 7. Suppose that the function f (x)=2-sin(e*) is continuous on with equal step 2'2 size, h equal to .…

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Q: 2. Find the (exact) values of a and b so that f is continuous at a = 2. 8r2 + 20x + 28 if x 2

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Q: d. Use the limit definition of the derivative, f (x) = lim f (x+h)-f(x) 1 +h)=j, to prove that VT =…

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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.