Write the word continuous if the given function is continuous on each of the given intervals otherwise write the word not continuous f(x)=x+5/x^-9 a.(0,9] b.(-3,3)
f(x)=x+5x−9=x+5x9,x≠0f is continuous on D(f) since it is a polynomialHence it is continuous on (0,9]It is not continuous on (−3,3) since it is not defined in x=0f\left( x \right) =x+\frac{5}{x^{-9}}=x+5x^9,x\ne 0\\f\,\,is\,\,continuous\,\,on\,\,D\left( f \right) \,\,\sin ce\,\,it\,\,is\,\,a\,\,polynomial\\Hence\,\,it\,\,is\,\,continuous\,\,on\,\,\left( 0,9 \right] \\It\,\,is\,\,not\,\,continuous\,\,on\,\,\left( -3,3 \right) \,\,\sin ce\,\,it\,\,is\,\,not\,\,defined\,\,in\,\,x=0f(x)=x+x−95=x+5x9,x=0fiscontinuousonD(f)sinceitisapolynomialHenceitiscontinuouson(0,9]Itisnotcontinuouson(−3,3)sinceitisnotdefinedinx=0
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