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1998test1

# 1998test1 - Physical Sciences Division University of...

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Unformatted text preview: Physical Sciences Division University of Toronto at Scarborough MATA26Y November 1 1, 1998 1 1 0 minutes TERM TEST I [14] 1. Using only the deﬁnition of derivative, ﬁnd f’ (m) for [15] 2. Evaluate the following limits: ( > 1' x a 1m — m—>0’ [:1:| sin 295 b 1’ ( ) cal—IR) cos 3x . em—zr—1 (c) 1m— [20] 3. (a) State the Mean Value Theorem (b) Give an example of a function which is continuous on [—2, 0] and to which the Mean Value Theorem does not apply. (c) Deﬁne formally what is meant by each of the following: (i) lim f(a:) : L \$~>a (ii) The function f (3:) is continuous at a: = a . d [15] 4. Determine d—y in each of the following cases: a: :53 + a: — 3 (a) y: sinx+ln\$ (b) yzln(sin(\$3+\$—3)) (c) lny+siny2\$3+m—3. [15] 5. Determine all intervals on which f (51:) : 3 315% + 35% is increasing and decreasing. [15] 6. Write the equation of the tangent line to f(:r) = mﬁ at .73 = 4. [6] The A+ Question Determine mango (x — In .73), if the limit exists. Justify your conclusion. ...
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