01. What is the domain of the following function? f(x) = (x + 3;x < 5 -3; x 2 5 Α. x +5 B. all real numbers C. x< 5 D. x < 5 E. not given

Q: 5а — 2 if x 10 If f(x) is a function which is continuous everywhere, then we must have b :

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Q: 2) Determine the intervals where the following function is concave down and concave up: f(x) = x³ +…

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Q: 2. Find the intervals on which the following function is increasing and those on which it is…

A: Function increasing when f'&gt;0 function decreasing when f'&lt;0

Q: Is the function f : Z→Z defined as f(n)=n^3+2 one-to-one ?

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Q: 4. If 0< f'(x)< for all x e R, show that f(-1) < f (1)<10+ f(-1).

A: Here we have to use property of increasing function . and Mean value theorem (MVT) Suppose f(x) is a…

Q: 2. Find the value of k so that the function Sa² + 25 |kæ – 40 is continuous at x = 5. defined by…

A: Given,          The function defined by fx=x2+25    x≤5kx-40    x&gt;5           is continuous at…

Q: (b) Let the function f: R → R defined by 3x for x > 3 2x2 + 3 for - 2 < x< 3 3 x? – 7 for x<-2 f(x)…

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Q: 5. The function f(x) is defined as: 4x3 +17x2 + 13x +36 x -4 ontinuous for all values of x. What…

A: solution:-f(x)=4x3+17x2+13x+36x+4     x&lt;-45x2+2x+a                       x≥-4f(x) is continuous…

Q: - Which of the following is not a possible f(x) = 4x - 2x + 10? 5 3 3, 5, 22

A: Given f(x)=4x5-2x3+10 Let x=3,  f(3)=435-233+10       =4(243)-2(27)+10=972-54+10=928≠0 3 is not a…

Q: On what interval(s) of x is f(x) positive?

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Q: Determine the numbers at which the function is continuous. 1. f(x) = x?(x + 3)² 2. f(x) = (x –…

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Q: 2. Consider the following function: y = f(x) = x" – 14x® (a) Determine in which regions this…

A: A function is increasing or decreasing that is determine by    f'(x)&gt;0 or f'(x)&lt;0 A function…

Q: 4- if f(x)= {† * *S S2 +x x 15 is this function is continuous or dicontinuous a) continuous b)…

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: buty What are all values of x for which the function f defined by f(x) = (x² - 3)e-* is increasing?…

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Q: Analyze the following graph of f' (x). Õver what interval is f concave down? 2 1 -4 -3 -1 4 -1 -2 -3…

A: Given  The graph of f'x  We have to find the intervals in which f is concave down.

Q: 4. Given the function f(x) = x3 In x. Determine the following: a. Domain b. X intercept(s)

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Q: x + 20 g(x) = { 3Cx + K if – 2 < x За — 2K if x < -2 | if 1 < x -

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 5. Suppose f(x) is an odd function. Prove that g(x)=f(x)| is an even function.

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Q: Find the absolute extreme values of the function on the given closed interval. 1 (x) = 10 + 27 x – x…

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Q: 3. Find the absolute extrema of the following function on the indicated interval. f(x) = x3 + 2x² –…

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Q: 1. Find the value of a that makes the following function differen- tiable for all x-values. Jax, if…

A: gx=ax,if x&lt;0x2-3x,if x≥0

Q: If f(x) be a function that is increasing on the interval (4,10). Over what interval is f(2x)…

A: f(x) is increasing from x = 4 to x = 10Lets change the variablef(t) is increasing from t = 4 to t =…

Q: 4. At what value or values of x will the following functions has/have removable discontinuities. х?…

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Q: 1. Find the value of c to make the following piecewise function continuous on the the interval (-o,…

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Q: 12. Find the value of k that will ensure that the following function is continuous at x = 3: x² + k…

A: As we know that the function is continuous at x=a if:   limx→a-f(x)=limx→a+f(x)=finite…

Q: 1) The function f(x) = x + 4 is odd True O False

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

Q: 11. What property must f(x) have in order for f'(x) to exist?

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Q: I need help trying to find the global max and min for the function  f(x)=(3^(1/3))-x on the…

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Q: 5. Consider the function g(x)=1 a) For what values of x is g(x) continuous? b) For what values of x…

A: In the question we have to find where function is continuous and differentiable.

Q: The domain of the function f(x)= tanh( x - 10) is Select one: O[-10, 10] O(0, ) None OR-{10} O [ 10,…

A: Set of values of x for which function is well defined is called domain of the function

Q: 7. Find the value of K that makes the function f(x) = (x² + 2 , x > 5 (x² – xk – 3 , x< 5 Continuous…

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Q: 1 For what value of x does the function f(x) = -x 4x attain the absolute maximum in the interval…

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Q: Given the graph of f(x) below, what is the open interval(s) over which f′(x) is negative?

A: The graph of f(x) is as shown below :

Q: 6. If a function f satisfies f(2) = 3, and – 3< f'(x) < 3 whenever 2 < x < 5, what is the range of…

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Q: 7. Decide if the following functions are one-to-one. Prove your answers.. (a) f(x) = x² – 1 (b) g(x)…

A: An injective or one one function is a function f that maps distinct elements to distinct elements;…

Q: 11 Consider the function, f (x) 2x 1 Use the above function to complete the following table. f(x) -1…

A: Explanation of the answer is as follows

Q: k. f(x) = /In(2x)

A: The solution for the answer is shown below.

Q: 1. Construct a table of values of the following functions using the interval of -5 to 5. a. g (x) =…

A: gx=x3+3x-5x2 When x=-5, g-5=-53+3-5-5-52=-5.8 When x=-4, g-4=-43+3-4-5-42=-5.0625 When x=-3,…

Q: ) = , 1 as x → 3+? What is true about this function f( x x2 -9 O f(x) O f(x) → 0 from below O f(x) →…

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Q: 1 Consider the function f(x) = 5 – x - Complete the following table of values, in which x< 5. 3 4…

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Q: Consider the piecewise function f(x) defined by 6 — 2х if x 4 х? — 16 For which x E R is f(x)…

A: Given function is fx=6-2x                            , if x≤4x-4x+4x-6x2-16    , if x&gt;4

Q: 9. Which function is greatest at x = 4 O A. f(x)= 3* O B. f(x)= 3(x) O C. (x) = x3 O D. none of the…

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Q: On what interval is the function f(x) = 4(x + 7)² +1 increasing? Sive your answer in interval…

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Q: 4. Suppose that f: X Y is a one-to-one function and that A C X and BC X. Prove that f (AnB) = f (A)…

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Q: (г? + 4х — 21) Let f(x) = for x + 3. How should f(3) be defined so that f will be continuous (л — 3)…

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Q: Which of the following is the x-coordinate of the relative extremum of the function f(x) = - 3x - -e…

A: Given: fx=-13e-3x-5x+47

Q: 5. Use the graph of the function f(x) below to estimate the open interval(s) on which f(x) is…

A: As per our guidelines, we are allowed to answer only one question. Since, u have posted multiple…

Q: Find the value ofk that makes the function continuous. f(x) = {avx+1 2х - а х<1) x2 1}

A: f(x) = ax+1    x≥1             {2x-a       x&lt;1}we have to find the value of a  for which function…

Q: 5) Find all points of inflection in the function g(x) = (x – 7) 13 on the interval [0, 10].

A: The points of inflection are those points at which the second order derivative of the function is…

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.