CalcNotes0205-page5

CalcNotes0205-page5 - / (Section 2.5: The Indeterminate...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
(Section 2.5: The Indeterminate Forms 0/0 and ± / ± ) 2.5.5 Solution to b) lim x ± 0 fx () = lim x ± 0 x 2 ² 1 x 2 ² x Limit Form ² 1 0 ³ ´ µ · ¸ = lim x ± 0 x + 1 = lim x ± 0 x + 1 x Observe: lim x ± 0 + x + 1 x Limit Form 1 0 + ² ³ ´ µ · = ¸ , and lim x ± 0 ² x + 1 x Limit Form 1 0 ² ³ ´ µ · ¸ = ²¹ . Therefore, lim x ± 0 does not exist (DNE), not even as ± or ±² . Commentary on b) • Here, the cancellation / dividing out of the x ± 1 factors merely makes it more convenient when we analyze the limit as x ± 0 . • Why does the limit not exist here as a real number?
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online