anonymous
  • anonymous
Which of the following functions is continuous at x = 3?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
anonymous
  • anonymous
D.all are continuos at x = 3
Michele_Laino
  • Michele_Laino
hint: the subsequent function: \[\Large f\left( x \right) = \frac{{{x^2} - 9}}{{x + 3}}\] is continuous at the subsequent set: \[\Large \left\{ {x \in {\mathbf{R}},\quad x \ne - 3} \right\}\]

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Haseeb96
  • Haseeb96
A is correct answer
anonymous
  • anonymous
isint c right too though?
Haseeb96
  • Haseeb96
no
UsukiDoll
  • UsukiDoll
Ah. I thought I misunderstood this. nevermind XD But yeah don't pick functions that are fractions because it causes restrictions and discontinuity.
UsukiDoll
  • UsukiDoll
I'll demonstrate why A is correct... |dw:1438416902248:dw| use difference of square formula for the numerator
UsukiDoll
  • UsukiDoll
|dw:1438416939205:dw| cancel out the x +3. Your new function is f(x) = x-3 and it's not a fraction, so all reals.
UsukiDoll
  • UsukiDoll
B and C are knocked out... for 2 reasons 1. piecewise function 2. jump discontinuity or point discontinuity is present in the graph. discontinuity occurs when there is asymptotic discontinuity there are gaps also known as jump discontinuity, or a hole is present (point discontinuity) .

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