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QveST [7]
3 years ago
6

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

Mathematics
1 answer:
Lina20 [59]3 years ago
8 0

Answer:

When we have a function like:

f(x) = \frac{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) = \frac{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} \frac{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} \frac{2*x+ 2}{ 2} = \frac{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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For all the values of x,<br> f(x)=x²+3 g(x)=2x-1 <br> a) find fg(2) <br> b) find gf(2)
erik [133]

Answer:

12 and 13

Step-by-step explanation:

(a)

To evaluate f(g(2)), evaluate g(2) then use the value obtained to evaluate f(x)

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f(3) = 3² + 3 = 9 + 3 = 12

--------------------------------------------

(b)

To evaluate g(f(2)), evaluate f(2) the use the value obtained to evaluate g(x)

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3 years ago
Marisol is cutting a 13.5-foot plece of ribbon for a craft project. She cuts off 4.5 feet,
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Answer:

Each remaining piece is 2.25 ft.

8 0
3 years ago
- 3 ( n + 5 ) = 12
scZoUnD [109]

Answer:the 1st one is N=17

THE SECOND ONE IS X=35

Step-by-step explanation:

hope this helps

6 0
3 years ago
Trigonometry pile up. Anyone mind helping me out with this one?
S_A_V [24]
cos34^o=\frac{8}{a};\ cos34^o\approx0.829\\\\\frac{8}{a}=0.829\to a\approx9.65\\\\9.65-2.5+3.6=10.75\\\\cos11^o=\frac{b}{10.75};\ cos11^o\approx0.981\\\\\frac{b}{10.75}=0.981\to b\approx10.55\\\\10.55-2.1+2.9=11.35\\\\c^2+3.8^2=11.35^2\\\\c^2=11.35^2-3.8^2\\\\c\approx10.69

10.69-3.2=7.49\\\\tan42^o=\frac{d}{7.49};\ tan42^o\approx0.9\\\\\frac{d}{7.49}=0.9\to d\approx6.74\\\\sin37^o=\frac{6.74}{e};\ sin37^o\approx0.602\\\\\frac{6.74}{e}=0.602\to e\approx11.2\\\\11.2+4.3=15.5\\\\sin53^o=\frac{f}{15.5};\ sin53^o\approx0.8\\\\\frac{f}{15.5}=0.8\to f\approx12.4

12.4-2.2=10.2\\\\g^2=10.2^2+1.7^2\to g\approx10.34\\\\cos21^o=\frac{10.34}{h};\ cos21^o\approx0.934\\\\\frac{10.34}{h}=0.934\to h=11.07\\\\11.07+1.7=12.77\\\\sin71^o=\frac{x}{12.77};\ sin71^o\approx0.946\\\\\frac{x}{12.77}=0.946\to x\approx12.1\ (cm)\leftarrow Answer

4 0
3 years ago
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