Which function has a point of discontinuity at x=3? A) x-3/2x^2 -2x -12 B) x+3/x^2 -6x +9. Please Explain why you chose the answer.

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Which function has a point of discontinuity at x=3? A) x-3/2x^2 -2x -12 B) x+3/x^2 -6x +9. Please Explain why you chose the answer.

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Answer 1 · 2018-01-25T14:56:35

B has discontinuity at $x = 3$ $x=3$

Explanation:

(A) In the function $\frac{x - 3}{2 x^{2} - 2 x - 12}$ $(x-3)/(2x^2-2x-12)$ , both numerator and denominator are equal to zero when $x = 3$ $x=3$ .

Then what happens when $x \to 3$ $x->3$ . For this let us find

$lim_(x->3)(x-3)/(2x^2-2x-12)$

= $lim_(x->3)(x-3)/(2x^2-6x+4x-12)$

= $lim_(x->3)(x-3)/(2x(x-3)+4(x-3)$

= $lim_(x->3)(x-3)/((2x+4)(x-3))$

= $lim_(x->3)1/(x+4)$

= $1/7$

Hence though $(x-3)/(2x^2-2x-12)$ is not defined at $x=3$ , we can still have value of $(x-3)/(2x^2-2x-12)$ at $x=3$ andhence, it is continuous.

(B) The function $(x+3)/(x^2-6x+9)=(x+3)/(x-3)^2$

Hence as $x->3$ , though nummerator tends to $6$ , denominator is $0$ and hence

$lim_(x->3)(x+3)/(x-3)^2=oo$

Hence $(x+3)/(x^2-6x+9)$ is not continuous at $x=3$

i.e. (B) has discontinuity

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Which function has a point of discontinuity at x=3? A) x-3/2x^2 -2x -12 B) x+3/x^2 -6x +9. Please Explain why you chose the answer.

1 Answer

Explanation:

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