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

A:

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: 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 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: 4.

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

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

A: