137_1314_HWA

# X0 x0 b lim f x does not exist and lim f xg x 0 x0 x0

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (x)g (x) does not exist. x→0 x→0 (b) lim f (x) does not exist and lim f (x)g (x) = 0 x→0 x→0 (c) lim f (x) does not exist and lim f (x)g (x) = 7 x→0 x→0 (d) lim f (x) does not exist and lim [f (x) + g (x)] does not exist. x→0 x→0 (e) lim f (x) does not exist and lim [f (x) + g (x)] = −2 x→0 x→0 8. Use the Intermediate Value Theorem to prove that the equation sin x = 2 cos2 x + 0.5 has at least one solution. 9. Prove the quotient rule (Theorem 3.2.11 on section 3.2 in the textbook). You can do two diﬀerent proofs: (a) Do a proof assuming both the Product Rule (Theorem 3.2.6) and the Reciprocal Rule (Theorem 3.2.9). (b) Do a direct proof using only the deﬁnition of derivative as a limit. (Look at the proof of Theorem 3.2.6 as inspiration.)...
View Full Document

## This note was uploaded on 02/09/2014 for the course MAT 137 taught by Professor Uppal during the Fall '08 term at University of Toronto- Toronto.

Ask a homework question - tutors are online