Using-approach-prove-that-lim-z-i-3z-4-2z-3-8z-2-2z-5-z-i-4-4i-Help-

Question Number 185243 by Mastermind last updated on 19/Jan/23

Using ε - δ approach prove that

li \underset{z \to i}{m} \frac{{3 z}^{4} - {2 z}^{3} + {8 z}^{2} - 2 z + 5}{z - i} = 4 + 4 i

Help!

Commented by Frix last updated on 19/Jan/23

Different approach, but :

3 z^{4} - 2 z^{3} + 8 z^{2} - 2 z + 5 = (z^{2} + 1) (3 z^{2} - 2 z + 5)

\frac{1}{z - i} = \frac{z}{z^{2} + 1} + \frac{1}{z^{2} + 1} i

\Rightarrow

\lim_{z \to i} \frac{3 z^{4} - 2 z^{3} + 8 z^{2} - 2 z + 5}{z - i} =

= \lim_{x \to i} (z + i) (3 z^{2} - 2 z + 5) = 4 + 4 i

Commented by Mastermind last updated on 19/Jan/23

Anyways, thank you but this is not

ε - δ approach

Commented by Frix last updated on 19/Jan/23

I know .

Since I^{'} m not The Omniscient Answering

Machine (if I were the answer would have

been 42 of course) I simply {don}^{'} t know the

ϵ - δ approach . You tell me please .

Answered by 123564 last updated on 19/Jan/23

Commented by Mastermind last updated on 20/Jan/23

Please try to be type, so itwill easily

to understand thank you