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How do you find the points of discontinuity of # y = ((x + 3)(x + 7)(x + 1)) /((x - 6)(x - 5))#?

Answer 1

This expression has discontinuities where the denominator is zero, which is when #x=5# and #x=6#.

Let #f(x) = ((x+3)(x+7)(x+1))/((x-6)(x-5))#

Both the numerator and the denominator are polynomials which in themselves are well behaved, continuous (infinitely differentiable) polynomials everywhere, but #f(x)# has severe discontinuities in the form of simple poles where the denominator is zero, which is when #x=5# and #x=6#.

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Answer 2

Eli Assouline

To find the points of discontinuity of the function y = ((x + 3)(x + 7)(x + 1))/((x - 6)(x - 5)), we need to identify the values of x that make the denominator equal to zero.

The denominator (x - 6)(x - 5) will be equal to zero when either (x - 6) = 0 or (x - 5) = 0.

Solving these equations, we find that x = 6 and x = 5.

Therefore, the points of discontinuity for the given function are x = 6 and x = 5.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.