Explain, using Theorems 4, 5, 6, and 8, why the function is continuous at every number in its domain. State the domain. sin x h(x) x + 1

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

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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: Determine if a function f : [0,2π] →Rdefined by f(x) = sin 2π is continuous.

A: Given function is f :[0, 2π]→R, f(x)=sin 2π

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

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

A: Given function

Q: use the Laws of Continuity and Theorems 2 and 3 to show that the function is continuous f (x) = x +…

A: Since, y=x is a continuous function Also, y= sin x is a continuous function

Q: Explain, using the theorems, why the function Is continuous at every number In Its domaln. x- 9 Q(x)…

A: Given: Q(x)=x-93x3-9 To find: The domain and Why the function is continuous at every number in its…

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

A: Note that the domain of g(x) is all real numbers and the domain of h(x) is also all real numbers. So…

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

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Q: Suppose that f(x) is a differentiable function such that f(8)=5 and f(8)-D0. If g(x)=sin(f(x)), then…

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Q: Use the definition of continuity and the properties oflimits to show that the function is continuous…

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

A: As we can see in below graph that the function is not defined at odd multiples of {pi/4} . So domain…

Q: Give an example of functions ƒ and g, both continuous at x = 0, for which the composite ƒ ∘ g is…

A: A function is said to be continuous at any point a, if A composite function is defined as a…

Q: Let f be defined piecewise as follows: kæ sin(x – 3) + 4, if ¤ < 3 f(x) = I – 3 4x2 + k, if æ 2 3…

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Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: Consider the given function: fx=x-1x-1 This can be written as a split function: fx=-1x&lt;11x&gt;1…

Q: Explain, using Theorem 4, 5, 7 and 9, why the function is continuous at every number in its domain.…

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Q: Is the following function continuous at x = 2? Explain why or why not. x2 +x – 6 - :x > 2 f(x) = x –…

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Q: In The given question, , determine whether the statement is true or false. If it is false, explain…

A: we have to tell whether the given statement is true or false. Statement : If a function is…

Q: Describe the interval(s) on which the function is continuous. (Enter your answer using interval…

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Q: Indicate whether the following statement is true or false. The function f (x) = |x| is continuous at…

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Q: lim 3i 4 +

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Q: Is the function f (x) below continuous on [3, +00)? (0, x > 0 X, 0 3

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Q: Suppose that f:R → R is a continuous odd function, such that 1 f(x) dx = 5 and -1 | f(x) f(x) dx =…

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Q: Let f(x) = sin(4g(x)). Evaluate f'(x).

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

A: Given f(x) is continuous.

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: B- If f(x) = is continuous at x = Find A? |Ax2 x2

A: The explanation of the answer as follows

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: Determine where f(x) is continuous, algebraically. Enter the answer in interval notation.

A: Given data: The expression for the given function is f(x)=log18(10x+150)-7x. The given function is…

Q: Let f(x)={tan(2x) ax+b if x>0 if x<0 For which values of a and b is f(x) differentiable for every…

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Q: Is f continuous at x = 2?

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Q: Locate the discontinuities of the function. (Let n represent an arbitrary integer.) 1 f(x) = V1-…

A: To find the discontinuities of the given function f(x)=11-sin(2x) we take denominator as zero ,  Now…

Q: What is the largest interval containing zero on which f (x) = sin x is one-to-one?

A: A function f: X -&gt; Y is said to be one-to-one, if the images of distinct elements of X under f…

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

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Q: Let f(x)={ tan-'(2x) ах+b if x20 if x<0 For which values of а and f(x) differentiable for every real…

A: Option second is correct, a=2 &amp; b can be anything.

Q: Which of the following functions are continuous? Why do you think they are continuous? hix fix

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Q: Classify the statement as either true or false. If f is continuous at x= 2, then f(2) must exist,…

A: Given query is to find statement is true or false.

Q: Is the following function continuous over all real values of 'x'? If applicable identify any…

A: Step 1:Given f(x) = X2 - 2x + 1.f(x) = (x-1)2 = y.When x = 0,     y = 1         y = 0,     x = 1

Q: Let f be defined piecewise as follows: kæ sin(x – 3) f(x) + 6, if x 3 For what value of k is ƒ…

A: Given,         f be defined piecewise as follows :         fx=kxsinx-3x-3+6 , if x&lt;36x2+k , if…

Q: Use the concept of composite functions to explain in detail why h(x) is a continuous function when…

A: Composite function

Q: Determine whether the statement is true or false. If f is continuous at 5 and f(5) 5 and f(4) = 3,…

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Q: Use the graph to determine the values of x at which the function is not continuous.   x=

A: Given the graph of the function

Q: For the shown function, find A so that the function is continuous at 1.

A: Consider the function: f(x)=x2          if x&lt;1Ax-3 if x≥1 . Theorem- The function is continuous…

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: Show that each function is continuous at the point indicated. 1. f(x) = 3x? – 4x + 2 at x = 2 2.…

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Q: Decide if the function below is continuous or not using the three conditions of continuity. { x*sin…

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Q: Determine what, if any, value to assign to f(a) to make f continuous at x2-5x+6 f(x) = %3D ;a= 3 x-…

A: We have to find the value

Q: Explain, using Theorems 4, 5, 6, and 8, why the function is continuous at every number in its…

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Q: Explain why the function is continuous at every number in its domain. State the domain. a)…

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