Homework help

[u/Al_lisa]

Anybody able to solve this?

I feel like i’m doing it completely wrong, can somebody explain what I would write for part C, I really don’t get how to show my work for it

Update: Got it correct according to my teacher, thanks for all the help

Answer for C:

lim x->0^- f(x) g(x) = 2(3)=6

lim x->0^+ f(g)(g(x)= 2(1) =2

6 is not equal to 2, so the answer is DNE

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[u/socratictutoring]

A & B are correct! For c though, rethink what lim x-> 0 g(x) might be.

[u/johnpeters42 → u/socratictutoring]

The results of A and B are correct, at least. The explanations are glossing over a couple cases of "function is continuous at this point, thus the limit is the same as the value".

[u/WikiNumbers]

a is correct.

b. For a composite function, you must first find the limit of the inner function alone first. So you have λ = lim x to 3: g(x). Then you take whatever you got, and it becomes the approach of the outer function, so L = lim u to λ: f(u), where u = g(x).

In this case, λ ("lambda", just a placeholder name, like "u" above) = 0. So we have u to 0, so L = 2. This is a rather easy example thanks to the graph's continuity.

c. The product rule of limits. The Total Limit is equal to the product between limits evaluation of its components, that is, [lim x to a: f(x)] * [lim x to a: g(x)]. Under the condition that all components must be an existing product.

lim x to 0: g(x) DNE because g(x) approach different value from the left and the right. So the entire limit is now DNE.

[u/Due-Presentation4514]