Continuous Functions - Apostal's One-Variable Calculus

[Shozaf Zaidi]

Homework Statement

A function f is defined as follows:
ƒ(x) = sin(x) if x≤c
ƒ(x) = ax+b if x>c

Where a, b, c are constants. If b and c are given, find all values of a (if any exist) for which ƒ is continuous at the point x=c.

Homework Equations

The Attempt at a Solution

I was unsure of how to start this problem at all. The solution provided in the back of the book is as follows:

a = (sin (c-b))/c if c≠0; if c=0 there is no solution unless b=0, in which case any a will do.

 

[RUber]

I think your solution may be typed in wrong.
Essentially, for the function to be continuous at c, the left side and right side must have the same value at c.
Or, the limit approaching from the left is equal to the limit approaching from the right.