Help !! Continuous functions

[Bill1432]

 

[Deleted member 4993]

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[HallsofIvy]

IF \(\displaystyle f(x)= 1+ e^{5- x}\) for \(\displaystyle 0< x\le b\) and
\(\displaystyle f(x)= 1+ e^{3x- 4}\) for \(\displaystyle b< x\le 5\).................................[edited]

We are told that f is continuous for all x and asked what b must equal.

Okay, Bill1432, what does "continuous" mean?

 

[pka]

IF \(\displaystyle f(x)= 1+ e^{5- x}\) for \(\displaystyle 0< x\le b\) and
\(\displaystyle f(x)= 1- e^{3x- 4}\) for \(\displaystyle b< x\le 5\)

It appears that Halls has a slight typo it should be \(\large 1{\color{blue}+}e^{3x-4}\) ...................................typo fixed

 

[HallsofIvy]

Thanks.

 

[JeffM]

This is just making more explicit Hall's hint.

If f(x) is continuous at x = b, f(b) must be a real number and the left limit must equal f(b).

What is the function to the left of b?

 

[pka]

This is just making more explicit Hall's hint. If f(x) is continuous at x = b, f(b) must be a real number and the left limit must equal f(b). What is the function to the left of b?

Why not just show this link?

 

[Steven G]

Try this link