   Chapter 2, Problem 7P

Chapter
Section
Textbook Problem

Find all values of a such that f is continuo us on ℝ : f ( x ) = { x + 1   if   x ≤ a x 2     if   x > a

To determine

To find: The value of number a.

Explanation

Result used:

The Quadratic formula of the equation px2+qx+r=0 is x=q±q24pr2p.

Calculation:

Given that f is continuous on , and f(x)={x+1    if   xax2       if   x>a

So f is continuous on (,a)(a,).

Since f must be continuous at a. Thus,

limxa+f(x)=limxaf(x)

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