Use the definition of "f is O(g)" to show that

Q: Consider the function f(x) = xn , where n is odd. Does f −1 exist? Explain.

A:

Q: Explain why the function g(x) = ln(4-x2) + square root of x+1 is continuous at every number in its…

A: Consider the given function g(x). The function g(x) is the sum of two functions f(x) and h(x).First…

Q: Sketch the graph of the function f(x). f(x) is continuous from the right at x = 3, but not from the…

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Q: Determine the domain of the function and prove that it is continuous on its domain using the Laws…

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Q: Find f(2) Is f continuous at x = 2? Explain your answer.

A: Given function

Q: How would you "remove the discontinuity" of f? In other words, how would you define f(2) in order to…

A:

Q: Find the numbers at which f is discontinuous. Show your work like in Example 34 from x2, x4

A: As per our company's guideline, we need to answer only one question at a time. Please repost the…

Q: Let f(x) = – 5 In(7x) f'(x) =

A: Given,           fx=-5ln7x

Q: In the given question/s, let f be a function that is positive and differentiable on the entire real…

A: Given, g(x)=f(x) Let f be a function that is positive and differentiable on the entire real number…

Q: determine where f is increasing. f (x) = |x + 1|

A:

Q: For function f, how would you remove the discontinuity? In other words, how would you define f(5) in…

A: For continuity limit of function at a point should be equal to functional value at that point.

Q: How would you "remove the discontinuity" of f? In other words, how would you define f(4) in order to…

A: Discontinuity of f can be removed by factorisation of the numerator

Q: Compute f'(a) for a = 3. f(x):

A:

Q: Consider the graph of f(x) below. Over what open interval is f'(x) positive? Give your answer in…

A: Given: The graph of the function f(x) is shown as: To find: The open interval where f'(x) is…

Q: Determine if f is continuous at x 9 from the right. [5x² f(x) = 3x-27 if x <9 if x29

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Q: Consider the function g :ℕ→ℝ  where  g(n) = 1 if n is odd and g(n) = 2 if n is even. Is g continuous…

A: Given function is g :ℕ→ℝ  where  g(n) = 1 if n is odd and g(n) = 2 if n is even.

Q: the given question/s, let f be a function that is positive and differentiable on the entire real…

A: It is given f  is positive and differentiable on the entire real number line and g(x)=In f(x) It is…

Q: determine where f is increasing. f (x) = x4

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Q: 7 Find the most general function F such that F'(): - 5V?.

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Q: se the product rule to evaluate f(x)g(x)| at x =

A: Given that: f(x)=2x3-8g(2)=5g'(2)=-3

Q: Determine whether  the following statement is true or false, and explain why. If ƒ″(x) &gt; 0 on an…

A: If the second derivative of a function f(x) is defined on an interval (a,b) and f ''(x) &gt; 0 on…

Q: a) Investigate whether the function f(z) = z is analytical?

A: In order to investigate whether the function is analytical or not, first write the function f(z) in…

Q: Let f(x)= 1 Use a 8- e proof to show that f is continuous at x = = 2. X-1

A:

Q: Describe the long run behavior of f(x) = x* As x → ∞, f(x) → ? As x → 0, f(x) → ?

A: This question is about function behaviour near infinity

Q: (b) Use the definition in (a) to compute f'(2) for the function f(x)

A:

Q: What can be said about f (3) if f is continuous and litn f(x) = ½?

A: Given f(x) is continuous.

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

A:

Q: How would you "remove the discontinuity" of f? In other words, how would you define f(2) in order to…

A: Given : fx = x2-x-2x-2

Q: Determine where the function f(x) is continuous. f(x) = /2-x

A: We have to determine where th function f(x)=(2-x)^(1/3) is continuous

Q: How would you "remove the discontinuity" of f? In other words, how would you define f(3) in order to…

A: The given function is: f(x)=x2-x-6x-3

Q: Let f(x) = 4 – a?, a > 0 f- (x) =

A: Given:- f(x) =4-x2  To find:- f-1(x)

Q: How to use the standard y = f(x) notation to indicate that (a, b) is an element of the function f?

A:

Q: Find the intervals on which the graph of f is concave upward. f(x) = In (x² – 2x + 10)

A: f(x)= In(x2 - 2x + 10) To find the intervals on which the graph of f is concave upward.

Q: Use the definition to find f' (a). Show all your work. 1 f(x) : x + 3

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Q: Find the interval on Which f` is increasing and the interval of which f`is decreasing

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Q: Explain, using the theorems, why the function is continuous at every number in its domain. 2x² - x –…

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Q: form the graph of f(x) into th 5) f(x) = x³ g(x) = -(x – 2)° %3D 3 %3D

A: We have to find

Q: Consider the function f(x) = 8+ (In(z² – 4))* What is its domain and range? (Use interval notation:…

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Q: Is the following function continuous at a = 1? Explain why. x2 +4x 21 - f(x) = ifx # 3 X - 3 6. ifx…

A: Consider the function  fx=x2+4x−21x−3              x≠36                                 x=3

Q: Use the IVT to show that f(x) = x 3 + x takes on the value 9 for some X in [1, 2].

A: Given- fx=x3+x To use- The intermediate theorem to show that the above function takes on the value 9…

Q: Redefine the function f to make it continuous at x = 0. -8x + 36 + x (х — 4) ; x + 0,4 f(x) = 4; x =…

A: Consider the condition for continuity.

Q: Assume that we have functions f(x) and g(x) so that

A: Given functions - ∫-13f(x) dx = -1∫35f(x) dx = 4∫-11g(x) dx = 3∫15g(x) dx = 2∫-152f(x)-5g(x)dx = ?

Q: Develop a general rule for f(n)(x) given f (x).…

A: the function given to us is    f(x) = xn

Q: Give an example of a function f : R → R that is continuous at x if x is an irrational number, but it…

A:

Q: How would you "remove the discontinuity" of f? In other words, how would you define f(3) in order to…

A: Given, fx = x2-2x-3x-3  We have to define f3 in order to make f is continuous at 3.

Q: Let f(x)= 6-x and g(x)= ln(x). What is the domain of g o f(x)? Express your answer in interval…

A: This question is based on functions and definition of Natural logarithm.

Q: Find e so that f(x) is continuous on the entire number line. if x3

A: fx=x2    if  x≤3cx    if  x&gt;3 Since the given function is a polynomial function for all x&lt;3…

Q: Explain why the Mean Value Theorem does not apply to the function f on the interval [0, 6]. f(x) =…

A: Given: f(x) = 1/(x − 3) and f in on interval [0,6]