Answer to Question #316399 in Calculus for Tina

Question

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)

Answer 1

$f\left( x \right) =x+\frac{5}{x^{-9}}=x+5x^9,x\ne 0\\f\,\,is\,\,continuous\,\,on\,\,D\left( f \right) \,\,\sin ce\,\,it\,\,is\,\,a\,\,polynomial\\Hence\,\,it\,\,is\,\,continuous\,\,on\,\,\left( 0,9 \right] \\It\,\,is\,\,not\,\,continuous\,\,on\,\,\left( -3,3 \right) \,\,\sin ce\,\,it\,\,is\,\,not\,\,defined\,\,in\,\,x=0$