Find a constant b such that h is continuous at x = 2, where x +1 for |x| < 2 h(x) |b – x² for |x| >2 With this choice of b, find all points of discontinuity.

Q: Find c such that the function x2 – 9 x с is continuous everywhere. - С —

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Q: Consider g(x) = x!/5. Is g(x) differentiable at x=0? Is g(x) continuous at x=0?

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Q: (a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

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Q: x< x3 B- If f(x) = Ax? is continuous at x = ; Find A? HIN IN

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Q: Find a value of a so that f is continuous at c = -3, or indicate this is impossible. x+3 x -3 f(x) =…

A: Given the function   f(x) = x+3-5x+3,  x≠-3a,                 x =-3   We need to find the value a…

Q: f(x)={x^2−9x≤c, 2x−10 x>c } i

A: Consider function f(x)=x2-9           x≤c2x-10        x&gt;c Now  limx→c+ f(x)=limx→c+…

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: Determine the domain of the function and prove that it is continuous on its domain f(x) = e - x 2

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Q: Find all values of "c" such that the function f(x) is continuous over  ( − ∞ , ∞ ) f(x) = 1 - x^2…

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Q: If f is continuousand ∫31f(x) dx=8, show that f takes on the value 4 at least once on the interval…

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Q: Given a continuous function of which is twice differentiable, if f" (c) > 0, which of the following…

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Q: (x²-x for x +0 If f(x) : and if fis continuous at x = 0, then k= 2x f(0) = k -1/2 O 1/2 O 1

A: f(x) = (x2 - x)/2x limx→0 x2-x2xlimx→0 x(x-1)2xlimx→0 x-12= -12

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Q: Assume that ƒ is continuous on [0,1] and that f(0) = 2 and f(1) = 1. Show that the graph of y = f(x)…

A: given  f is continuous on [0,1] f0=2,f1=1y=x2+1

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: g(x) = sec(x) %3D

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Q: Consider g(x) = rº/3. Is g(x) differentiable at x=0? Is g(x) continuous at x=0?

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

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Q: Let f(x) be a given continuous function on a closed interval [a, b]. Use the Extreme Value Theorem…

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Q: If a function f is continuous at 0, show that g(x) = xf(x) is differentiable at 0 and find the value…

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Q: 57. Find a constant b such that h is continuous at x = 2, where for |x| 2 With this choice of b,…

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Q: a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

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Q: Let f(x) be a given continuous function on a closed interval [a, b]. Use the Extreme Value Theorem…

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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: Find a constant b such that h is continuous at x = 2, where h(x) = {x + 1 for lxl &lt; 2 b - x 2 for…

A: Given, hx=x+1x&lt;22b-x2x&gt;2

Q: Q3) For what values of a and b are -x² + a , x Continuous at every x ?

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