# Continuity (ii)

• Dec 13th 2009, 06:21 AM
nameck
Continuity (ii)
f(x) = { [(e^x) - 1] / x ; if x not equal 0
...... .{ b ...................; if x = 0

What value of b makes f continuous at x = 0?

so.. the left side and right side must be equal in order to make
f continuous at x = 0

[(e^x) - 1] / x = b
[(e^x) - 1] = (b)(x)
e^x = (b)(x) + 1
.
.
.
dont know how to proceed..

should i introduce ln?
• Dec 13th 2009, 06:32 AM
HallsofIvy
Quote:

Originally Posted by nameck
f(x) = { [(e^x) - 1] / x ; if x not equal 0
...... .{ b ...................; if x = 0

What value of b makes f continuous at x = 0?

so.. the left side and right side must be equal in order to make
f continuous at x = 0

No, $\frac{e^x-1}{x}$ is not defined at x= 0. It is the limit of that that must be equal to b in order that the function be continuous.
Take the limit, perhaps using L'Hopital's rule, to find b.

Quote:

[(e^x) - 1] / x = b
[(e^x) - 1] = (b)(x)
e^x = (b)(x) + 1
.
.
.
dont know how to proceed..

should i introduce ln?
• Dec 13th 2009, 06:57 AM
nameck
got it!!
b = 1
correct?