We know that it is true that “If it is raining, then the sidewalk is wet”. Common sense tells us that it is also true that “If the sidewalk not wet, then it is not raining.” In calculus, we learned that it is true that “If f is differentiable at x = a, then f is continuous at x = a”. (1) What does common sense allow you to conclude? (2) Is it true that “If f is continuous at x = a, then f is differentiable at x = a? Explain.

Q: Show that f(x) = x² + 12x +41 -2 -x² 12x - 31 ifa >-6 2 if x < -6 if x = -6 has a removable…

A: The given function,The aim is to prove the function has a removable discontinuous at  and redefine…

Q: Is the function f (x) = x* – x| odd, even, or neither even nor odd? Odd Even Neither even nor odd

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Q: True or False, and give a short reason: (a) If a function is differentiable, then it is continuous.…

A: Given problem:- True or False, and give a short reason:   (a) If a function is differentiable, then…

Q: (c) If f(x) is continuous on a closed interval [a, b] and f(x)dx > 0, then f(x) > 0 for some x E [a,…

A: Since you have asked multiple questions in single request.so we will answering only first question.…

Q: Solve the equation, inequality, or system of equations.

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Q: Problem (3) Show that if a continuous function f is holomorphic outside a line in C then it is…

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Q: differentiable on the open interval (-2, 5), and (A) There is a number e in the interval (-2, 5) for…

A: Since you have posted multiple questions and we can answer one question. So, answered first…

Q: If f(x) is continuous everywhere, then If(x)| is continuous everywhere. TRUE O FALSE

A: If f(x) is continuous everywhere, then |f(x)| is continuous everywhere.True of false.

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: If f(x) is continuous everywhere, is it true that |f(x)| is also continuous every- where? What about…

A: Consider two functions as hx=x and gx=fx.

Q: For what value of the constant c is the function f continuous on (-∞, 0)? cx? + 2x if x < 3 f(x) = {…

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Q: 1. Read pages 46 - 54 Section 1.5 Continuous Functions in your textbook and take notes below by…

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Q: Consider the following argument: If f(x) is a differentiable function, then it must be continuous.…

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Q: Mathematicians I. Perepelitsa and C. Douglas are having an argument. Professor Douglas claims that…

A: According to the Intermediate Value Theorem, if a function f(x) is continuous in [a,b] and has the…

Q: If f is a continuous function on (-4, 4) whose graph is in 1. ƒ"(x) > 0 on (-4,-2) 2. (0, 1) is an…

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Q: Question No: 5 Taking three different examples, justify that every continuous function is not…

A: Continuous function: A function is said to be continuous function if both left hand limit and right…

Q: Suppose f is a continuous function with x = a in its domain. Part 2 of the Fundamental Theorem of…

A: Note:- As per our guidelines, We’ll answer the first question since the exact one wasn’t specified.…

Q: (a) By the Fundamental Theorem of Calculus, Part 2, sec2 xdx tan(x) |5 = |3| (b) The Mean Value…

A: Given statement is: by the Fundamental theorem of calculus, ∫0πsec2xdx=0 According to the…

Q: the following function is a continuous function at x=2 امرفق x² +x-6 x+ 2 x) = x2 - 4 x = 2

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Q: 2. Rewrite each of the implications below using all 4 forms: (1) only if, (2) is sufficient, (3) is…

A: (a) If a function f is differentiable, then f is continuous.Only if: Only if f is continuous, is f…

Q: 3. (a) If f: X→ Y and g: Y→ Z are functions and go f is one-to-one, must f be one-to- one? Why/Why…

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Q: mod can be applied if the function is continuous only.

A: We have to check whether the Fibonacci method is applied if the function is continuous only.

Q: 1. Determine whether these statements are always true or sometimes false. (a) The function f(x) |a-3…

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: The definition of continuity of a function at a point. • The definition of the limit of a function…

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Q: (-2, 2), |(0,1) (3.0) -5-4 -3 -2 3. (-2, -1), (3,-1) Which statement is true ? f(x) is not…

A: Topic :- Continuity True option = A