Answer to Question #314460 in Calculus for sam

Question #314460

Determine whether the following functions are continuous on the given interval. Show your complete solution.

1. Ζ’(π‘₯)=√4βˆ’π‘₯2 ;[βˆ’2,2]

2. Ζ’(π‘₯)=3π‘₯2 βˆ’π‘₯+5 ; (βˆ’βˆž,+∞)


1
Expert's answer
2022-03-21T15:41:45-0400

f(x)=4βˆ’x2f\left( x \right) =\sqrt{4-x^2} is continuous on D(f)=[βˆ’2,2]D\left( f \right) =\left[ -2,2 \right] , since it is a composition of polynomial function 4βˆ’x24-x^2 and power function x\sqrt{x}

f(x)=3x2βˆ’x+5f\left( x \right) =3x^2-x+5 is continuous on (βˆ’βˆž,+∞)\left( -\infty ,+\infty \right) since it is polynomial function.


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