Expert: Paul Klarreich - 10/8/2009

Question
find the number c that makes f(x) into:
1. a continuous function
2. a differentiable function
in one case f(x) approaches f(a) at every point in the other case delta(f)/delta(x) has a limit at every point.

f(x)= sinx  x<1
     c     x> or equal 1

Answer
Questioner: masood khan
Country: Pakistan
Category: Calculus
Private: No
Subject: calculas
Question: find the number c that makes f(x) into:
1. a continuous function
2. a differentiable function
in one case f(x) approaches f(a) at every point in the other case delta(f)/delta(x) has a limit at every point.

f(x)= sinx  x < 1
    c      x >= 1
.........................................
Hi, Masood,

(Have you settled down, yet?)

1. c = sin(1) will do it.

2. Nothing will do it.  If you change to:

f(x)= sinx  x < pi/2
    c      x >= pi/2

then, okay.  c=1 would do it.