Question #301990

1.graph the height of a right triangle as a function of the base ,if the hypotenuse is fixed at 10.


2.graph the diameter of a circle as a function of it's circumstances.


3.determine whether the following function is continuous or discontinuous .


f(x)=3x+2/x^2-6


a.at x =-1


b.at x =-2


1
Expert's answer
2022-02-24T17:01:33-0500

1.

y=100x2,{0<x<10}y=\sqrt{100-x^2},\{0<x<10\}



2.


y=xπ,x0y=\dfrac{x}{\pi}, x\ge0


3.


x260x^2-6\not=0

x=6,x=6x=-\sqrt{6}, x=\sqrt{6}

a.


f(1)=3(1)+2(1)26=15f(-1)=\dfrac{3(-1)+2}{(-1)^2-6}=\dfrac{1}{5}

limx13x+2x26=3(1)+2(1)26=15=f(1)\lim\limits_{x\to -1}\dfrac{3x+2}{x^2-6}=\dfrac{3(-1)+2}{(-1)^2-6}=\dfrac{1}{5}=f(-1)


The function f(x)f(x) is continuous at x=1.x=-1.


b.


f(2)=3(2)+2(2)26=2f(-2)=\dfrac{3(-2)+2}{(-2)^2-6}=2

limx23x+2x26=3(2)+2(2)26=2=f(2)\lim\limits_{x\to -2}\dfrac{3x+2}{x^2-6}=\dfrac{3(-2)+2}{(-2)^2-6}=2=f(-2)


The function f(x)f(x) is continuous at x=2.x=-2.



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