Let X denote the amount of time in hours that a battery on a solar calculator will operate adequately between exposures to light sufficient to recharge the battery. Assume that the density for X is given by: -3 f(x) f(x)=(25/3)x³ 2

Q: Show that Ф (X) %3 Ф»(Х" ). fг e erime e prime

A: We solve this question using a well known inversion formula for cyclotomic polyomials. The solution…

Q: Compute the average rate of change of g(x)=1/x over the interval [1, 1+x]. Simplify the expression…

A: To Compute the average rate of change of g(x)=1/x over the interval [1, 1+x].

Q: Compute the average rate of change for g(x) = 4x on the following intervals: %3D A) 0sxs1 B) [-1,1]…

A:

Q: Estimate g(1.2) − g(1) if g'(1) = 4.

A: Given: g'(1)=4 Now, Using the Linear approximation formula:

Q: uppose ƒ (x) = mx + b and g (x) = mx2 + b. Find the average rate of change of each function on the…

A:

Q: Let g(x) = 2. Use small intervals to estimate g'(1). Round your answer to two decimal places. g'(1)…

A:

Q: If f(x)=5+2(x-1)^1/2, does f(x) satisfy all the conditions of the mean value theorem in the interval…

A:

Q: d dx f(x) = ex, f(0) = 8.

A:

Q: Use logarithmic differentiation to find f'(x) for f(x) = x %3D Select one or more: O a. x(x*-) O b.…

A:

Q: The average value of the function f(x)=x²-19 on [0,9] is

A:

Q: Let g(x) = log3(æ). Find g'(4). g '(4).

A:

Q: Expand f(x) = (1+x)^1/2 to the linear order of x and estimate the error when 0<x<1/2.

A: Step 1:Step 2: Step 3: Step 4:

Q: Use a comparison test to determine whether I (ln(x) — 1) dx converges or diverges.

A: (i) If f(x)≤g(x),∀x∈[a,∞) and ∫a∞g(x)dx is convergent,  then ∫a∞f(x)dx is convergent. (ii) If…

Q: 8. Use the Mean Value Theorem to prove fEC'la, b], f'(x) = 0 = f(x) = c

A: see below the answer

Q: QUESTION 3 Find the value of for which the average value of f(x)=3x²-8x+3 on the interval [0,b]…

A:

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

A: