21.L. Let f be in Class C' on a neighborhood of a point c in RP and with values in Rr. If Df(c) is one-one and has range equal to Rº, then there exists a positive number 8 such that if x – c| < 3, then Df(x) is one-one and has range equal to Rr.

Q: 1) Evaluate the absolute extrema of the following functions on the given interval. S(x)=(x² +3x)³…

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Q: 9. 3 If f is continuous and f (u) du = 3, then / (4xf(x²) + f(3x)) dx is equal to

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Q: - { S 1² – 3 if r -1 2. Determine the constant k such that the function f(r) is continuous at r =…

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Q: 7. A function f (x) is continuous on the closed interval [2,5] withf (2) = 17 and f(5) = 17. Which…

A: Rolle's theorem

Q: Hello! What is the solution to this question? Thank you for your help! Have a nice day :)

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Q: Suppose f(x) is the function such that for a > 0 we have f(x) = (e" – 1) In(x) and for x < 0 we have…

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Q: 2.if f (x) = x2 + 3, with domain R then f(x) has f(x) %3D O T F

A: Here the given function is f(x)= x2+3 with domain R We need to find it has inverse or not.

Q: 2. (a) Suppose that f is a differentiable function such that |f'(x)| < c for every x. Show that for…

A: To Prove: a. If f is a differentiable function such that f'(x)≤c for every x.Then for any real…

Q: 5. Show that the function h(r, y) defined by if + y 1 is discontinuous.

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Q: For what values of a and b will f(x) be continuous on everywhere at x = 2 if the function is x² – 4…

A: f(x)=x2-4x-2x&lt;2ax2-bx+32≤x&lt;32x-a+bx≥3

Q: 16. Suppose that f is differentiable at c and that f'(c) + 0. Show that there exists a ð > 0 such…

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Q: ,15 15 ** Let f be a continuous function. If f(x)dx = 15 and f(x)dx = -8, then f(x)dx equals -5 В C…

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Q: 1- Discuss the continuity of the following functions at given poin { V9r4+x² 5x2+3x+1 (a) f(x) = if…

A: It is given that

Q: 8. Suppose that f is a continuous function such that f'(x) > 0 for all æ, f(0) = 0, and f(1) = 1. If…

A: f'(x)&gt;0 for all x, f(0)=0 and f(1)=1.To Find: If ∫01f(x)dx=13, find the value of ∫01f-1(x)dx.

Q: 7. Suppose that f: R → R is continuous at c and that f(c) 0 such that f(x) < 0 in the…

A: Recall the definition of continuity around c .And then choose an ∈&gt;0 to get a δ&gt;0…

Q: Suppose f(1) is continuous everywhere, and has the following values: 10 20 30 40 f(z) -4 9. 11 3. 7…

A: Given,  f(x) is continuos everywhere  f(x) has the following valuesx010203040f(x)-491137To…

Q: Зx2 — 1 Q7- Let f(x){ cx + d Vx + 8 if x 1 Determine e and d so that f is continuous everywhere (as…

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Q: 4 Suppose that f(1) 3, f(4) = 5, f '(1) = 4, f '(4) = 2, and f " is continuous. Find the value of xf…

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Q: 1. Suppose f is a function which satisfies f(x + y) = f(x) + f (y) for all x,y e R. What is the…

A: Let f is a function which satisfies f(x+y) = f(x) + f(y)  for all x,y∈R   f(x+y) = f(x) + f(y) ,   ∀…

Q: (8) Suppose f(x, y) = -x + y², x = s² +t°, y = 2s – 3t. Compute f, when s = 1 and t =-1. %3D

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Q: 4.1 Suppose that fig and g'are continuous on the interval 1= {x :asxs b). Show that a ) exists, and…

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Q: 2. Supposethat f(x)=?βx? −3 if βx + 2 ifx≤2 x &gt; 2Find the value of β so that f(x) is continuous…

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Q: 45. For what value of a is x2 - 1, x < 3 2ax, f(x) = %3D 2ах, continuous at every x?

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Q: 3. Find the points of relative extrema of the following functions on the specified domain: (a)…

A: Introduction: Evaluation of maximum and minimum value of a function is one of the most important…

Q: 7. Suppose that f: R R is differentiable at c and that f(c) = 0. Show that g(x):= |f(x)| is…

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Q: 4. Find the maximum value of f (x) = In(x – In x) on the interval -sse. e

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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: If f:R→R is a continuous even function, then | F(x)dx is necessarily equal to -5 O10 O Cannot be…

A: A function is even if f(-x)=f(x)

Q: 8 Ay 10- Compute the following estimate of f(x) dx using 8- y = f(x) the graph in the figure. 6-…

A: Consider the graph of the function

Q: 2. Compute / f(x)dx for the following function. O if x 0 f(x)

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Q: 5. Use Green's Theorem to evaluate f. $ (y² – 4x) dæ – (2+ x²y²) dy where C - - is shown below. y…

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Q: 16.C. If f is defined and continuous on R? to R and if f(xo) > 0, then is f positive on some…

A: Consider the provided question,   We need to show that, f is strictly positive on some neighborhood…

Q: Suppose that f(x, t) is the probability of getting x suc-cesses during a time interval of length t…

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Q: 2. Find the values of the constants a and b for whichf is continuous everywhere if ax + b, f(x) =…

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Q: 10.C. If f is defined and continuous on R to R and if f(xo) > 0, then is f positive on some…

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Q: 3. Suppose that {f(t)} = F(s) with F a differentiable function and that L{f'(t)} Exists. Then…

A:

Q: 1. If y = f(x) is a continuous function for all 0 < x< 6, and f(0) = 1 and f(6) = 7, then which of…

A: Function

Q: Suppose F(x) is between 4 and 8 for x in [3,12]. What is the largest that · 12 L" F (x) dx can be?

A: given that function F(x) between 4 and 8 for x in [3, 12] we have to find the largest value of…

Q: Suppose f is known to be differentiable and contains a local extremum at c, then which of the…

A:

Q: 8 Ay 10- f(x) dx using Compute the following estimate of 8- the graph in the figure. 6- S(4) 4- 2-

A: The given graph is  To find ∫08fxdx using Simpson's Rule with n=4

Q: 3. Define f(2) in a way that extends f(s) = -8 to be continuous at s = 2. s2 – 4

A:

Q: 11. Suppose f(x) dr = 4, f(x) dx = 5, and | f(x) dx = –1. Then f(x) dx =

A: From given data: ∫03fxdx=4 .....1∫23fxdx=-1 .....2 From (1) and (2): f3-f0=4  .......3f3-f2=-1…

Q: A continuous function y f(x) is known to be negative at x = 2 and positive at x=7. Why does the…

A: Given that f(x) is a continuous function.

Q: - 35) Prove that if y=flx)is continuoUS and flx1= 0 when x is a rational number, then f Lx)=0 for…

A: The objective is to show f(x) =0 for all x belongs to R.

Q: if x1 O No, since g(x) is undefined at x=1. O Yes, and g'(1)=3. O Yes, and g'(1)=8. O No, since g(x)…

A: Given

Q: 7.14. Show that if f = u+iv is analytic in a region S and u is a constant function (i.e.,…

A: Analytic function which is a constant

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

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Q: a) Evaluate in terms of Gamma function ∫e^(−y^2) y^13 dy   limit 0 to ∞ b) Find ∫f(x) dx limit: 1…

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Q: 15. If f+g is differentiable at a, are f and g necessarily differentiable at a ? If f g and f are…

A: Let f be any function that is not differentiable  at the point a and define as: gx=-fx for all real…

Q: 22 + a For what value or values of k is f(x) = ka + 3k - 5 continuous at a = 5?

A: NOTE: Refresh your page if you can't see any equations. . to find the undefined point, take…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.