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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.)...
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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.
 Fall '08
 UPPAL
 Calculus, Sets

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