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# 6th - 8 Given 2 x 3-3 y 2 = 8 ﬁnd d 2 y dx 2 9 When a...

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Math 119 Recitation 6 October 21, 2006 1. Evaluate the following limits or explain why they do not exist. (a) lim x 2 | x - 2 | | x |- 2 . (b) Let 5 - x 2 f ( x ) 5 - x 3 for - 1 x 1. Find lim x 0 f ( x ). (c) lim x 1 1 - x 3 1 - x . (d) lim x →∞ x +sin x 2 x +7 - 5 sin x . (e) lim x 0 x + x cos x sin x cos x . (f) lim x 0 { x [sin ( x - 5 ) + 1] + x 2 cos ( 2 π x ) } (g) lim x 2 sin ( 1 x - 1 2 ) 2. Use the formal deﬁnition of the limit to prove the followings: (a) lim x 1 ( x 3 - 2 x 2 + x + 5) = 5 (b) lim x →∞ 1 x 3 - 1 = 0 3. Find y 0 for the following curves: (a) y = tan 2 x +1 x - 1 . (b) y = x - 1 x +1 . (c) y = 3 x 2 - 1 x . (d) y = tan q 1+tan q . 4. The curve y = ax 2 + bx + c passes through the point (1 , 2) and is tangent to the line y = x at the origin. Find a, b, c . 5. Is there a value of b that will make f ( x ) = ± x + b if x < 0, cos x if x 0, diﬀerentiable at x = 0. 6. Given f ( u ) = u 5 + 1, u = g ( x ) = x , ﬁnd df dx | x =1 . 1

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7. Show that (2 , 4) lies on the curve x 3 + y 3 = 9 xy ; then ﬁnd the tangent and the normal line to the curve there.
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Unformatted text preview: 8. Given 2 x 3-3 y 2 = 8, ﬁnd d 2 y dx 2 . 9. When a circular plate of metal is heated in an oven, its radius increases at the rate of 0 . 01cm/min. At what rate is the plate’s area increasing when the radius is 50cm. 10. Approximate (a) 3 √ 1003 (b) (1 . 002) 100 11. A and B are walking on straight streets that meet at right angles. A approaches the interseciton from north at 2m/sec.; B moves away from the interseciton to east at 1m/sec. Let θ be the angle at B of the triangle OAB , where O denotes the intersection point. At what rate is θ changing when A is 10m away from O and B is 20m away from O . 2...
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6th - 8 Given 2 x 3-3 y 2 = 8 ﬁnd d 2 y dx 2 9 When a...

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