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Illusion [34]
3 years ago
9

The average rate of change of f(x)=3x+9 is 9. true or false?

Mathematics
1 answer:
MA_775_DIABLO [31]3 years ago
7 0
The rate of change is the slope.
f(x) is the same as y...
f(x) = 3x + 9.....y = 3x + 9....and in y = mx + b form, the rate of change(slope) can be found in the m position.

y = mx + b
y = 3x + 9....so the slope or rate of change is 3...not 9...so answer is false
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Answer with Step-by-step explanation:

We are given that

f(x)=\left\{\begin{matrix}\dfrac{x^2-2x}{x^2-4}&,if\ \ x\neq 2 \\ 1&,if\ \ x=2\end{matrix}\right.

We have to explain that why the function is discontinuous at x=2

We know that if function is continuous at x=a then LHL=RHL=f(a).

f(x)=\frac{x(x-2)}{(x+2)(x-2)}=\frac{x}{x+2}

LHL=Left hand limit when x <2

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Right hand limit =RHL when x> 2

Substitute

x=2+h

\lim_{h\rightarrow 0}f(x)=\lim_{h\rightarrow 0}\frac{2+h}{2+h+2}=\lim_{h\rightarrow 0}\frac{2+h}{4+h}

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