SOLUTION: I am not sure how to work this out. I would appreciate any help. Thanks! Let "c" be a number and consider the function f(x) = { ax^2 -5, if x <1

Question 944970: I am not sure how to work this out. I would appreciate any help. Thanks!
Let "c" be a number and consider the function f(x) = { ax^2 -5, if x <1
c, if x =1
(1/x)-2a, if x > 1 }

a) Find all numbers for "a" such that lim x-> 1 f(x) exists
b) Is there a number "c" such that f(x) is continuous at x=1?

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
For the limit to exist, as you approach from the left () must equal as you approach from the right .

.
.
.
For it to be continuous then,

That way the limit from the left, the limit from the right and the value at x=1 are all the same which is the definition of continuous.

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