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65. Is there a number a such that3x2 ax a + 3lim+x-2exists? If so, find the value of a and the value of the limit.

Question
65. Is there a number a such that
3x2 ax a + 3
lim
+x-2
exists? If so, find the value of a and the value of the limit.
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65. Is there a number a such that 3x2 ax a + 3 lim +x-2 exists? If so, find the value of a and the value of the limit.

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Step 1

Refer to the question, we have to find the number ‘a’ such that limit exists .

3x2aa3
lim
x2
x- 2
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3x2aa3 lim x2 x- 2

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Step 2

Then the provided limit can be written as,

3x2 a3
lim
2 2x -x -2
3x2aa+3
lim
x2
3x2axa+3
= lim
x2x-x2
3x2axa+3
lim
(x+2)(x-1)
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3x2 a3 lim 2 2x -x -2 3x2aa+3 lim x2 3x2axa+3 = lim x2x-x2 3x2axa+3 lim (x+2)(x-1)

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Step 3

As the limit exists so (x+2) must be a factor of 3x2+a...

3x2aa3
At,x-2
3(-2)a(-2)+ a+3 0
12 2aa3 0
a = 15
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3x2aa3 At,x-2 3(-2)a(-2)+ a+3 0 12 2aa3 0 a = 15

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Tagged in

Math

Calculus

Limits

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