Discontunuity of f(x) = x^2 plus 2x over x plus 2

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Answer 1

Answer:

Answer:

When we have a function like:

$f(x) = (g(x))/(h(x))$

This function will have a discontinuity only if it diverges, and a divergence can happen when the denominator is equal to zero and the numerator is different than zero.

In this case, we have the equation:

$f(x) = (x^2 + 2*x)/(x + 2)$

Here the denominator is:

h(x) = x + 2

This is equal to zero when:

x + 2 = 0

x = -2

Now we need to see what happens with the numerator when x = -2

g(-2) = (-2)^2 + 2*(-2) = 0

Is equal to zero.

Then we need to see the limit when x -> -2, and use the L'Hopital theorem.

$\lim_(x \to \ - 2) (x^2 + 2*x)/(x + 2)$

Because we have zero over zero at that point, we need to look at the quotients of the derivatives of both numerator and denominator.

$\lim_(x \to \ - 2) (2*x+ 2)/( 2) = (2*-2 + 2)/(2) = -1$

Then the function does not diverge, then the function has no discontinuity.

We also could look at the graph of f(x) to see it:

Our function is a linear function, and this is because the numerator is x times the denominator, then the function is:

f(x) = x.

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Answer:

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Sally has decided to purchase a used car. The car costs $5800, she was able to pay $500 down; she was also able to secure a 3-year loan at 7.5%. She knows that she can afford to spend a maximum of $200 on a car payment each month. Write the Excel function that would tell her the maximum amount she could borrow

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Answer:

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Divide 6/13 by 6/12 .

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6/13÷6/12=
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What is the slope between two points 12,6 and 20,22

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The slope of a line between 2 points is given by the formula

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slope is 2 hoe it helped

Trapezoid PSTK is isosceles. SK = 20, SH = 12, If ST = 1 4 HK, find HK, APTSK, m∠P, and PS. Find HK, Area of pstk, HK and PS

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Answer:

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