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Asked Sep 9, 2019
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2.5.47
For what value of a is the following function continuous at every x?
a x 12a, x23
f(x)
15,
x<3
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
(Simplify your answer. Use a comma to separate answers as needed.)
A. a
O B. There is no solution.
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2.5.47 For what value of a is the following function continuous at every x? a x 12a, x23 f(x) 15, x<3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Simplify your answer. Use a comma to separate answers as needed.) A. a O B. There is no solution.

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Expert Answer

Step 1

Refer to the question,

The function provided is,

x)ax12a,x23
15, r <3
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x)ax12a,x23 15, r <3

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Step 2

For function to be continuous Left hand limit at that point should be equal to Right hand limit at that point which should be equal to function value at that point.

lim f(x) im f(x)= f(a)
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lim f(x) im f(x)= f(a)

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Step 3

Now use the above concept to...

lim f(x15
lim f(x)ax-12a = f(3)
ax -12a 15
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lim f(x15 lim f(x)ax-12a = f(3) ax -12a 15

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Calculus

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