Question

Math Analysis (Calculus)-
!Please let me write it out!
Given:

Answer 1

Given: \[f(x)=(\frac{ 1 }{ x }-\frac{ 1 }{ x^2 })\]
a. Explain why the following is incorrect:\[\lim_{x \rightarrow 0^+}f(x)=\lim_{x \rightarrow 0^+}(\frac{ 1 }{ x }-\frac{ 1 }{ x^2 })=\lim_{x \rightarrow 0^+}(\frac{ 1 }{ x })-\lim_{x \rightarrow 0^+}(\frac{ 1 }{ x^2 })=(+\infty)-(+\infty)=0\]
NOTE: IT IS INSUFFICENT TO SAY THAT INFINITY-INFINITY MAY NOT EQUAL TO ZERO!!!

Answer 2

@SolomonZelman

Answer 3

you are dealing with different orders of infinity

Answer 4

My teacher said that we need to be very brief with that explanation.

Answer 5

And sorry i don't know what you mean by different orders