BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 2, Problem 7P
To determine

To find: The value of number a.

Expert Solution

Answer to Problem 7P

The value of number a is 1±52.

Explanation of Solution

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)limxa+x2=limxa(x+1)a2=a+1a2a1=0

By using Quadratic formula

a=(1)±(1)24(1)(1)2(1)  =1±1+42=1±52

Thus the value of number a is 1±52_.

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