The limit of the following infinite sum can be evaluated using a definite integral. (1+ i) n 4 lim f(x)dx. n3 a In the integral, a = 1 f(x) = 4x3 The limit of the infinite sum is (1 + i) n 4 lim = | f(æ)dæ - n3 a 15

Q: Which of the following expressions has a domain that is a subset of the domain (i.e. set of all…

A: We can find the domain of each function and then find the answer.

Q: Use the graph of f(x) shown below to answer each question.

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Q: a. The population P() of a culture of bacteria is given by P(t) = 5000(2)4, where t is the time in…

A: Given P(t)=5000(2)t4 Basic function with base e is y=a(e)x Lets pick up some points from the given…

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Q: Find where the function is increasing. 2 y = x² - 3lnx, (x > 0)

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Q: For what value of k will the function f be continuous on (-∞, ∞)? f(x) = = +2 9 x + 3 k if x # -3 if…

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Q: Which of the following can be considered a "power function?" Select all that apply. f (x) = 2x f (x)…

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Q: Let X be the amount of time (in hours) the wait is to get a table at a restaurant. Suppose the cdf…

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Q: Given the function below, find the point of inflection: y=a* _ 2p2 OP() O P(-1,-1) OP() O None of…

A: Given problem:- Given the function below, find the point of inflection:   y = x4 - 2x2

Q: Find all real zeros of the function. f(x)=-3(x-4)²(x+7)³ If there is more than one answer, separate…

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Q: 2 int () if –10<x<0 g(x)= -5 if x = 0 -0.5x +4x if 0<x<10

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Q: Approximate the area under the graph of F(x)=0.6x³ +6x² -0.6x-6 over the interval [-8,-3] using 5…

A: F(x)=0.6x3+6x2-0.6x-6 a=-8b=-3n=5

Q: for n = 235, we have s(235) = 2^2 + 3^2 + 5^2 = 38. determine whether the function s(n) is an…

A: A function or mapping from X→Y is said to be (a) Injective OR One-One:--A function is said to be…

Q: 6. Find the intervals on which f(x) = 2.x – 3x? – 120x+6 is increasing or decreasing. %3D

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Q: 2. Which expression is equivalent to * 2(x- 4)2 – 2 2x - 16x+ 32 2x + 16x – 32 Option 1 Option 2 2x…

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Q: For what value of k will the function f be continuous on (-∞, ∞)? x² 2 f(x) = = x + 3 k if x # -3 if…

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Q: find the greatest value of the function within the intervals f(x) = /(1– x² )(1+2x²) in [–1,1].…

A: Let's find.

Q: Use the graph of f′ shown in the figure to answer the following. (a) Is f(3) − f(2) &gt; 0? Explain.…

A: a) From given graph it is observed that, f' is positive in region (0, 4). So f(4) &gt; f(0).…

Q: (5) Given f(x) -2r and h(x)= simplify using the following operations: Write answers in standard…

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Q: 1+3x-1 2. lim x-0

A: We have to find the limit .

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Q: (x³ + 2x² + 1) dx x+2

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.