# How do you prove that the limit #(3x + 5) = -1# as x approaches -1 using the formal definition of a limit?

We cannot prove it. It is not true. We can prove that

Preliminary analysis

Look at the thing we want to make small. We want to see the thing we control in the thing we want small..

Now we need to actually write up the proof:

Proof

We can condense a bit

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the limit #(x+5)(1/(2x)+1/(x+2))# as #x->1#?
- How do you find the Limit of #(sin^3 x) / (sin x - tan x)# as x approaches 0?
- How do you evaluate the limit #(1/2+1/x)/(x+2)# as x approaches #2#?
- How do you find the limit of #x/sin(x)# as x approaches 0?
- How do you prove the statement lim as x approaches 0 for #x^3=0# using the epsilon and delta definition?

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