Q(A). Let {fn(x)}-1 00 n%=D1 be a sequence of functions (1+ (x – 2)* S, - defined over [2,3]. Show that: (a) fn(x) is meaurable and monotonic increasing for all n.

Q: 2x Let f (x) = x+3 Then f is increasing over R*. False True

A: We will check for the sign of first derivative If f'(x)≥0 , then f(x) is increasing If f'(x)≤0 ,…

Q: Select all functions increasing for x>0. Of(2) = O f(x) = VE |f(x) = 0 O f(x) = x O f(x) = |x| Of(2)…

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Q: 1 h(s) = (s – 10)2 Find the largest value of A such that the function h(s) is increasing for all s…

A: Given: h(s) = 1s-102  Increasing interval :(-∞ , A ). The function f(x) is increasing on an interval…

Q: Consider the sequence of functions {fn(x)} = {n²x(1 – x)"} for x € R and n = 1, 2,3.... (a) Sketch…

A: The given sequence: {fn(x)}={n2x(1-x)n} for x∈ℝ and n=1,2,3,... Choose x=0.5∈ℝ.   a) Sketch on the…

Q: Let f(x) = ln x and g(x) Show that f(x) and g(x) are both increasing when x > 0. Vr.

A: Given, f(x) = lnx When f(x) is increasing then f'(x) > 0  Differentiating f(x) with respect to x…

Q: Find the domain, local max/min, and inflection points (if any) of the function f(r) = r* In(x).

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Q: Let f(x) be the piecewise function -2x + k f(x) = { x² + 1 if x < 1 if x ≥ 1

A: for continuous function

Q: Consider the function f: N→ N given recursively by f(0) = 2 and f(n + 1) = 3. f(n). Find f(11)…

A: Given that f(0)=2f(n+1)=3f(n)f(1)=3f(0)=3*2=6f(2)=3f(1)=3*6=18f(3)=3f(2)=3*18=54and so on…

Q: Let t represent the total number of hours that a truck driver spends during a year driving on a…

A: Probability of at least one accident = p(t) Probability of no accident = 1 - p(t)

Q: (4ах + 2b , X<1 2х — 3Ь,1 <х < 3 (2ах + 4b g(x) ,3 <x Find the values of "a" & “b" if gm is…

A: We will find the value of a and b as following-

Q: 3- Find the value of k So that the function f is continuous at the indicated point: (kx², if x 2…

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Q: G(n) = (d)o(d) is multiplicative function. If p is prime then G(p*), fork >1 equals dịn Select one:…

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Q: Consider the following equation defining the function f on the integers implicitly: f(n) = n+ f(n –…

A: Given:            f(n) = n +f(n-1),  f(1) = 1

Q: 2x is an increasing function for x>0. 2+x Show that y = In (1+x)-

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Q: 1 ㅠ<2, x#1 |x-1| h.

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Q: Evaluate the function f(x) = e* + In (x + 3) at c, where –2.5 < c < 2. (Give your answer as an…

A: Given a function, f(x)=ex+ln(x+3) To find the interval of function at c.

Q: Which functions meet all 3 criteria? . f is increasing on the interval(-∞0, 0) f is bounded above.…

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Q: does the function f(x) = e^10|x - 2| - x^2 have an absolute maximum? If so, find it. what about an…

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Q: Let P=f(t)=600(1.033)t be the population of a community in year t. Evaluate f(10)

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Q: x - 2 Evaluate f (x) = at x = 2. %3D X - 2 Select one: A. Continuous B. Discontinuous

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Q: x + a x+b It will be decreasing all throughout its domain if b> a. It will be increasing for x- b.…

A: Given function: fx=x+ax+b