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# Determine the value of ‘k’ for which the following function is continuous at x = 3:

*(CBSE 2017)*

*(CBSE 2017)*

Answer :

Since f(x) is continuous at x = 3.

**Expanding using the formula: (a + b)**

^{2}= a^{2}+ b^{2 }+ 2ab

Now, factorizing (x^{2} + 6x - 27) such that the product is 27 and difference is 6, we get,

(x^{2} + 6x - 27) = x^{2} + 9x - 3x - 27 = x(x + 9) - 3(x + 9)

(x^{2} + 6x - 27) = (x -3) (x + 9)

Therefore,

⇒ 12 = k

Thus, f(x) is continuous at x = 3, if k = 12.

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