Find the value of c such that (-)- { S22 - c²;. x <4 cx + 20; x > 4 is continuous on the real numbers.

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A: A function fx defined on an open intervala,b is uniformly continuous on a,b iff  i fx is continuous…

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A: The given function is  f(x) = x+2ifx&lt;02x-2ifx≥0

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Q: Use interval notation to indicate where x2 – 1 - f(x) = x2 – 7x + 6 - is continuous. f is continuous…

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Q: Evaluate (x by Simpson's rule breaking it into 6 intervals. 1 2+x2

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

Q: Every continuous function on a, b\, that has absolute extrema on endpoints, must have one .(a, b)…

A: b. False Consider a continuous function f (x) on [a, b], that has absolute extrema on the endpoints.…

Q: For what value of k will the function f be continuous on (-∞, 0)? { x2 – 16 if x + -4 f(x) = x + 4 k…

A: We have to find

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Q: Suppose that ?(?) is continuous and differentiable on the interval [0,6], that ?(6) = −7 and that…

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Q: Find the largest open intervals where the function is concave upward. 16) f(x) = x3 - 3x2 – 4x + 5…

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Q: Find the largest open intervals where the function is concave upward. f(x) = x 3-3x2 - 4x + 5 O None…

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Q: [3, 5]. - Calculate Rg for f(x) = 7 – x over R8

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Q: II. Determine if Vx2 – 3x – 4, if x 1. is continuous or not at x = -1 and at x = 1. In the case of…

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Q: Find the extreme values of f(r) = Vr(5 – x) in the interval [–1,3].

A: For extreme points we need to find critical points and check value of f(x) on boundary values of…

Q: (b) Verify Mean Value Theorem for f(x)= 3x² – 7x – 4 over the interval[–1,4] .

A: Given: fx=3x2-7x-4

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Q: Show that f(x) = is uniformly continuous by definition on the interval (-1,1) . 4 - *

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Q: Find the values of a and b that make f continuous everywhere.

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Q: If f is integrable on the interval

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Q: If f (s Continuous then on -fex) True or felse?

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Q: If Зх — 2,х <3 -{ - h(x) х4 — 74, х 2 3 Is h(x) continuous at (x=3)? 1 Add file

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Q: Consider the following. f(x) = |x < 1 |x|21 Find the x-values at which fis not continuous. Which of…

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Q: For what values of a, m and b does the function x = 0 0 < x < 1 1< x< 2 3, f(x) = -x² +3x + a, тх +…

A: to find the values

Q: How many continuous functions f are there which satisfy (f(x))² = x² for all x?

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Q: is the net signed area between f(x)=2x+2 and the x-

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Q: Find the values of a and b that make f continuous everywhere. x2 - 4 if x < 2 X - 2 ax2 - bx + 1 4x…

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Q: Determine the interval(s) for which f(x) =- - 2x2 is concave down. 12

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Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the calue of c…

A: Given function is

Q: . Determine the upper bound on the error in the approximation: x2sinx3 x. - if x|<0.8 6.

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Q: iii If the discontinuity of ƒ is removable, redefine ƒ so that it's continuous at 0

A: This question related to the topic continuity of real analysis.

Q: A. is definiteand continuous, B. is indefinite and continuou C. is discontinuous and definit D. is…

A: Given: To explain the correct option of the given statement as follows,

Q: Let f(x) = vV72 – x and g(x) = x² – x. Give the domain of f o gusing interval notation.

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Q: Use the definition to prove that the function in f(x) = 2x - 3 is uniformly continuous.

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Q: Suppose that f(1) = 5, ƒ(4) = -8, f'(1) = 4, f'(4) = -2, and f" is continuous. Find the value of |…

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Q: Comment on the continuity of f(x) at x = -2, x = 0 and x = 3 If discontinuous, what is the type of…

A: At x=-2, L.H.L.=limx→-2-fx=2R.H.L.=limx→-2+fx=-1f-2=2 Since L.H.L.≠R.H.L., therefore the limit does…

Q: Show that the f(x)=x-(In x)^{x} =0, has at least one solution in the interval [4, 5].

A: There are more than one question. We will solve the first one. Given, f(x)=x-[ln(x)]x, we need to…

Q: Find the values of a and b that makef continuous everywh x2 – 4 - if x 3 a = b =

A: A function f is continuous when x=c is the same as saying that the function's two-side limit at x=c…

Q: let Peas be delimed by Xく2 3-X I5 fixo continuous V= 2 2.

A: A function is continuous at a point if it's left hand limit is equal to right hand limit and both…

Q: Determine where f(x): V4 - x2 is continuous. Express the answer in interval notation.

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Q: Fix a constant r>1 Using the Mean Value Theorem that enx > 1 + x for any fixed x >0 prove

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Q: Find the values of m and n that make f(x) continuous over (-∞, ∞): f(x) = m= n= 4 x-2 mx² - nx 2x -…

A: Topic- Limits and continuity

Q: 29 - For uhat values of a and b is ax+2b x+3a- b くXS2 3X-5 Continuous at every X ?

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Q: Suppose fx) is continuous on the interval [0,10] and that f(x) = 0 only when x = 4. If f(5)< 0, what…

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Q: 3. Show that 5 x + 7 is a continuous fimction

A: Let, f(x) = 5x+7 be defined over R, the set of all real numbers. Choose an arbitrary point c in R.…