Thread: calculus help on Limits and epsilon delta

Hi, I do need your help with the question attached above.

I do have another question:

Prove by the eplison delta method

Lim of X^4 when x approaches -2 equal to 16

Originally Posted by guess

Hi, I do need your help with the question attached above.

I do have another question:

Prove by the eplison delta method

Lim of X^4 when x approaches -2 equal to 16

I'll do the problem.



The objective is to find such that whenever .

Note that .

Let us supposed . We find the upper bounds on and



.

Thus, .

If we take , the proof is complete.

Does this make sense?

hi,

correct me if i'm wrong:

|X^4-16|= |(X+2)(X-2)(X^2+4)|

|X-2|=|X+2-4|<|X+2|+|-4|

we let delta less then 1

|X+2|< 1

|X-2| < (3)+(4) = 7

|X^2-4+8|<|(X+2)(X-2)+8|<|X+2||X-2|+|8| = (1)(5)+8 =13

from here,

|X^4-16|= |(X+2)(X-2)(X^2+4)|< delta(7)(13) = 91 delta

91 delta = epsilon
delta = epsilon/91.

We chose the min delta {1, epsilon/91}

Originally Posted by Chris L T521

If we take , the proof is complete