Question

find b so that f(x) is continuous

Answer 1

\[\left\{ x^2-3,\rightarrow 0<x \le b\right\} \left\{ \frac{ 6 }{ x } \rightarrow x>b\right\}\]

Answer 2

i know the value by using a calculator, buy how can i find it by hand? i just found the intersection point of both functions, if i set the functions = to each other, i get x^3 - 3x - 6 = 0 but how do i solve that?

Answer 3

@ParthKohli

Answer 4

@.Sam.

Answer 5

@goformit100 @nincompoop

Answer 6

you want the left limit and the right limit to be the same as x approaches b

Answer 7

in other words you want: \[\lim_{x \rightarrow b^-}(x^2-3)=\lim_{x \rightarrow b^+}\frac{6}{x}\]

Answer 8

your inequality given says b>0 so we do not have to worry that 6/x is discontinuous on the interval x>b

Answer 9

so the next step since both functions are continuous on the intervals (and well polynomials are continuous everywhere on their domain) is to just plug in b to evaluate the limits. Then solve the resulting equation.