Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. If a function is left-continuous and right-continuous at a, then it is continuous at a. b. If a function is continuous at a, then it is left-continuous and right-continuous at a. c. If a 6 b and ƒ1a2… L … ƒ1b2, then there is some value of c in 1a, b2 for which ƒ1c2= L. d. Suppose ƒ is continuous on 3a, b4. Then there is a point c in 1a, b2 such that ƒ1c2=1ƒ1a2+ ƒ1b22>2.

Q: For what value of the constant c is the function f continuous on (−∞, ∞)? f(x) =    cx2 + 6x…

A: fx=cx2+6x     if x<3x3-cx       if x≥3 fx is continuous for all x<3 & x>3, because it…

Q: Let f(x)={mx−17 if x<−10               {x^2+3x−7 if x≥−10 If f(x) is a function which is…

A: Topic = Functions

Q: Consider the following statements: (i) There exists a function f: R → R which is discontinuous at…

A: Note : A function f is said to be continuous at a point c if lim f(x) x→c = f(c) .

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Q: Determine whether each of the following functions is (a) continuous (b) differentiable.

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A: Curve fitting and concavity

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A:

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Q: 1) Find the values of a and b that make f continuous everywhere. x' - if x<2 х—2 f (x) = { ax? –…

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Q: Determine the intervals of continuity for the following function. AY 5- 4- 3- 2- 14 0+ 1. 2 3 4 6. 5

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Q: If F is continuous on the set of real numbers, then A True B) False

A: The solution is given in the next step.

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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: (x – 2)2 +1 if x 2

A: We have to check continuity of function at x=0 and x=2

Q: Suppose f(x) is continuous everywhere, and has the following values: 10 20 30 40 f(æ) 10 - 2 12 - 6…

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Q: On which of the following intervals is f(x) = x-2 1. continuous? A (-0, +x) B [2, + ) © [1,2] D none…

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Q: Is the following piecewise function continuous? if x < 0 0<if x < 3 if 3 < x f(x) = -3x² x - 3, . -x…

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Q: Determine if the following functions are continuous at the given value of x. Show your solutions. 1.…

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Q: Determine whether the followingstatements are true and give an explanation or counterexample.Assume…

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Q: For what value of a is the following function continuous at every x? a?x f(x) = х+ 2а, х22 12, x<2

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Q: For what value of a is the following function continuous at every x? x - 153, x< 17 f(x) = ax, x2 17

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Q: On what intervals are the following functions continuous? g(x) = x3/4

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Q: | Find the values of a and b such that the following function [a(x − 1)² + b²x+2, if x 3, ious at x…

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Q: On what intervals are the following functions continuous? a.ƒ(x) = x^(3/4) b. h(x) = x^(-1/6)

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Q: О 1,3] O [-3, -1] О (1,3] O [-3, -1)

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Q: 9. ✓ (at x = ()) (at x=-2) 10. ✓ 2 (for all values of x) (at x = 3) 8.

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A: Solve the following

Q: On what intervals are the following functions continuous? a.ƒ(x) = x^(1/3) b. h(x) = x^(-2/3)

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Q: 3. Which of the following functions is continuous?

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A: Here we have to state whether the statement is true or false.

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Q: a) Let f : X → Y be a function such that f-1 : Y → X is a closed function, where a closed function…

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Q: The function f(x) is continuous everywhere. FALSE O TRUE 3.

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Q: Let f(x)={4x−4 if x≤6               {−5x+b if x>6 If f(x) is a function which is continuous…

A:

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.