Find a value of k for which g(x) is continuous everywhere: x2 – 9 g(x) : x + 3 3 kx : x =

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Q: Determine whether k(x) is continuous at r = 3, where x + 3, x 2.

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Q: Suppose that a continuous function g satisfies: g(x)dx = 42 and g(2x)dx = 3. %3D 2 Find æg(3x²)dx.

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Q: • Use the IVP to prove that r3 – 4z+2 has a zero in the interval [0, 1] • Use the IVP (and a similar…

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Q: If f(g(x)) is continuous at 0, then g(x) is continuous at 0  true or false

A: Given that If f(g(x)) is continuous at 0, then g(x) is continuous at 0

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Q: Find number k so that f(z) = 10x + 8 x -1 is continuous on (-0,0). O -2 4 -4

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Q: Find c such that the function Sx2 – 4 - 4 x c is continuous everywhere. c =

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A: We will check the continuity of the function

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Q: Sketch the graph of a continuous function y = h(x) such that a. h(0) = 0,–2 < h(x) < 2 for all x,…

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Q: Find a value of k making h(x) continuous on [0, 5]. kx 0 < x < 2 x + 1, 2<x < 5 h(x) =

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Q: . Find a value of k so that the following function is continuous at x = 1. f(x)%3D x<1 x-1 2kx, x21

A: Given: The given function                                             To find: The value of k, such…

Q: ) For what value of a is fx² -1 x<3 S(x)= { |2ax x23 Continuous at every x?

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Q: Find a value of k making h(x) continuous on [0, 5]. kx , 0 < x < 1 h(x) = x +3, 1<x < 5

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Q: Find c such that the function x ≤ c { is continuous everywhere. f(x) = x² - 3 X 6x 12 x > c -

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Q: Find c such that the function 10 I C - is continuous everywhere.

A: A function f(x) is said to be continuous at a point x=a if limx→af(x)=f(a). That is, a function f(x)…

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A: Topic = Functions

Q: Find the values of a and b such that the following function a² cos(x − 2) — 26(³-x), if x 2, is…

A: Topic = Limits

Q: Find c such that the function ² - 4 x c is continuous everywhere.

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Q: 13. Let g be defined by V7x +2 V6x + 4 | g(x) = if x 2 - and x 2 x – 2 k , if x = 2 For what value…

A: The given functiong(x)=7x+2-6x+4x-2,if x≥-27 and x≠2k,if x=2

Q: Suppose that a continuous function g satisfies: | g(x)dx = 12 and g(2x)dx = 27. Find æg(3x²)dx.

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Q: If f(x) = a #0 and f is continuous, the value of k is 2x k x = 0 o 1 o 1 2 1/2

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Q: Determine if g (x) = is continuous at x = 0

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Q: Which values of C makes r(x) (a) left-continuous, (b) right-continuous (c) continuous x2 +3 for x 2

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Q: f(x) = x – 3x² + x – 7 is continuous everywhere. - false true

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Q: If ƒ(x) is continuous [-00,b]then on ſf(x)dx= lim [ ƒ (x)dx а. a a

A: Explanation of the solution is given below...

Q: For what values of h and k is h+2x , 15 x52 -2 < x<-1 2< * 2 - Continuous at every x ? 2x2 - 2x-4,…

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Q: Find c such that the function x c is continuous everywhere. x² – 8 f(x) = {

A: ANSWER : c = 5