What is the lim as x--->2 of g(f(x)) with reference to this diagram:
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My reasoning thus far is that there is no limit because as x approaches 2 in the first graph, f(x) approaches 0. But in the second graph, of g(x), the function is not continuous at x = 0.
Is it DNE?
This question is free game for anyone. In regards to the diagram referenced in the first post, to which I posted a link, is the value of c that makes [f(x) + c g(x)] exist equal to the same value of c that makes f(x) + c g(x) continuous at x = 1.
I approached the problem this way:
For to exist, both the left and right limits must exist.
(The question mark is there not because this limit is unknown, but I leave it to you to figure it out.) Also, the left and right limits must be equal to each other. After finding the second limit, set the two of them equal to each other, and solve for c.
Now refer to the definition of continuity to complete the question, and proceed in a manner similar to above.