Find the value of the constant a for which the following function is continuous: 5(4 – x²) - X if x < 2 f(x) = x – 2 5x + a if x > 2 a) -30 b) -18 c) -20 d) -12 e) None of these

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A: f is continuous and  To evaluate the integral , we will use the following substitution

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A: We have to find the points at which f is continuous. Polynomial function is continuous every where

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A: NOTE: Refresh your page if you can't see any equations. . find the left-hand limit of the function…

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A: To show: For any constant k, ddxf(x)k = f'(x)k

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A:

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A:

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A: Topic:- calculus

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A:

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A: Given: fx=cx2+2x,x&lt;22x+4,x≥2 We know that any given functionfx will be continuous at x=a if,…

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A: To find out the sum a+b.

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A:

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A: Given that the functions f,g and g' is a continuous function on the interval defined as  I=x:a≤x≤b…

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Q: ind the values of c that make f continuous everywhere: { Sa² – c² if x 3

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A:

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A: From the given function it can be observed that it is continuous for all values of x less than 5 and…

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A: The given function is: f(x)=-4+-48-6x

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A:

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A: Since the function is continuous at every real number , so, it is also continuous at x=5Therefore,…

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A: Given that the function f(x). Here we find the value of a and b to make f is continuous everywhere.

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Q: Find the values of a and b that make f continuous everywhere: x²-4 if x 3 -

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: Given,  over the interval  .

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A:

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A: Given fx=x2-8x+16x≤3ax+bx&gt;3 is differentiable everywhere so it is also continuous.

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A:

Q: Suppose that f(x) is continuous and differentiable, f(2) = -2, f(6) = -6, and f(x)dx =-10. Compute ,…

A: Topic:- Functions

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A:

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A:

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A: This is problem of limit and continuity. Based on the general formulas and concepts we will answer…

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A: ANSWER : c = 5

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A: