MATHEMATICS HIGH SCHOOL

Identify whether each value of x is a discontinuity of the function by typing asymptote, hole, or neither. 5x/ x3 + 5x2 + 6x

Answers

Answer 1

Answer:

Answer:

Function is discontinuous at

x=0 (Hole)

x=-3 (Vertical asymptote)

x=-2 (Vertical asymptote)

Step-by-step explanation:

Given: $f(x)=(5x)/(x^3+5x^2+6x)$

We need to identity the discontinuity of the function. As we know function is discontinuous where it is not defined.

So, The function is discontinuous at hole, asymptote and break point.

$f(x)=(5x)/(x^3+5x^2+6x)$

$f(x)=(5x)/(x(x^2+5x+6))$

$f(x)=(5x)/(x(x+3)(x+2))$

For hole, we will cancel like factor from numerator and denominator.

At x=0 we get hole.

For vertical asymptote, we set denominator to 0

x+3=0 and x+2=0

Vertical asymptote:

x=-3 and x=-2

Function is discontinuous at

x=0 (Hole)

x=-3 (Vertical asymptote)

x=-2 (Vertical asymptote)

Answer 2

Answer:

Answer:

asymptote

hole

neither

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Answers

Answer:

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Answers

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Answers

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Answers

Answer
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Explanation
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Answers

Answer:

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