P MT 13

# P MT 13 - lt-ilath 1A l‘v’Iidterni 1 2:00pm-3:30pm You...

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Unformatted text preview: lt-ilath 1A l‘v’Iidterni 1. 2004-9-31] 2:00pm-3:30pm You are allowed 1 sheet of notes. Calculators are not allowed. Eaeh question is worth 1 mark. whieh will be given onlv for a elear eorreet answer and correct working. There is no partial eredit for wrong answers. There are questions on both sides of the paper. 1. Find the domain of the funetion ﬁx] 2 afar — 4. 2. Sketeh the graph of y = |;r‘2 — 1|. 3. Find a formula for the inverse of the function y = eﬁ. 4. Determine the inﬁnite limit (+3: or —oc) of l_ :r—I—1 1m —. x—xe 333(1? — 1] . Evaluate the limit CI! _ r2 —:r —2 11m — x—r—l ;r—|—1 6. Find the eonstant e that makes g eontinuous for all reals. where Elli} = 3:2 — e2 if;r <1: 4. gm) 2 o1r—I—20 if;r 4. 7'. Find the numbers at whieh f is discontinuous. where f is deﬁned by =:r+1 if;r~:: U.f(\$)=e1" ifU ;r 1, f(ilf) 22—1? ifzr :5 1. 8. Evaluate _ . Lira — 3 11m :r—*+DC- 3:3 — ;r —|— 10' 9. Find the equation of the tangent line to the curve y = :r3 at the point where ;r = 1. 10. Sketeh the graph of a funetion for which f{0) = U. f’{0] = —1. f[1} = U, f’ﬂ) = —1. 11. Determine for What valuea ef;r the funetien f[:r) = :r|:r| ie differentiable and ﬁnd a formula for f’. 12. Differentiate the function y = Gar—333. 13. Find all points on the curve y = 11:3 —|— 33:3 —|— 31? —|— 1 Where the tangent ia horizontal. 14. Differentiate [I3 —|— lje‘f. 15. Differentiate ...
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