7. (12) Show that the hypotheses of the Mean Value theorem are satisfied and find all values satisfying the conclusion for 3 – z2 if r<1 f(x) = 1 on {0,2]. ifr>1

Q: 6. If f(x) satisfies 0 < f(x) < x for 1 < x < 3, what is the maximum possible value of the average…

A:

Q: 2. (a) Let A = {x = [0, 1]: x has a decimal representation not containing the digit 5.} Show that A…

A: We shall use certain results from measure theory

Q: Q1 Let X1,.,X, f(r;0) = )0"(1 - 0)2-,x = 0,1,2. (i) Find the score and information functions of 0.…

A: Let, X1,x2,...,Xn be the random samples having following distribution: f(x;θ)=2xθx(1-θ)2-x  ;…

Q: (3-x² if x ≤ 1 if x > 1 Theorem is satisfied. Then find all values of c 2. For the function f(x) = -…

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Q: 8. Is the set of functions f₁(x) = 3e³x and f₂(x) = -3e3³* independent? Show using the -3.x…

A: Given functions- f1x=3e3x  and  f2x=-3e-3x To show whether the given set of functions is independent…

Q: 8. Using the Mean Value Theorem and Rolle's Theorem, show that3 + x – 1 =0 has exactly one real…

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Q: 18. Let f(x)=2- |2x - 1. Show that there is no value of e such that f(3) -f(0) = f'(c)(3-0). Why…

A: We have given that f(x)=2-|2x-1|for x&gt;12f(x)=2-(2x-1)=-2x+3f'(x)=-2for…

Q: 2. Let F(x) = x – sin(3x) on the interval [0, #]. (a) Explain why F satisfies the conditions of the…

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Q: For what value of a, m and b does the function { 3 x = 0 -x2 + 3x + a 0 < x < 1 1< x < 2 g(x) = mx +…

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Q: 2 13) Consider f(x)= x<o 12x+1 0≤x≤2 Determine whether f is continuous on [0,1] and [1,2]

A: solution of the given question is like as:

Q: 8. What is the value of c guaranteed to exist by the Mean Value Theorem if m(x) = x4 - 3x over the…

A: The answer for the above question is as shown below.

Q: Q1 Let X1,.,X, f(r;0) = ()0 (1 – 0)2-, x = 0,1,2. (i) Find the score and information functions of 0.…

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

Q: 4.

A: Check that f(x) is continuous &amp; differentiable on the interval. Find the values of c The main…

Q: (x +3)³ 4(x – 1)2 12 16 11 Consider the function f(x) Note that 4 4 1 (x – 1)2 - | (x – 9)(x + 3)²…

A: Solve by mean value theorem

Q: 2. Let f(x) = -x– 1. a) Find f-1(x).

A:

Q: 4. a) Suppose that for some specific problem, heuristic function h is admissible. Is h? admissible?…

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Q: 4. Show that In sin 6 d0 = – n 2 by applying the mean-value principle to In |1+ z| for |2| <r < 1,…

A: ∫0π2logsin(θ)dθ=12∫0πlogsinθdθ                         =12∫0π2logsin2θdθ…