HW4-510-soln

# HW4-510-soln - AMS 510 HW4 Solution 6.52(a x 2 y 2=C(b xy...

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AMS 510 HW4 Solution 6.52 (a) x 2 y 2 = C (b) xy = C (c) tan 1 y x 1 = C

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(d) x 2 / 3 y 2 / 3 = C (e) x 2 4 y 2 16 z 2 = C (f) sin x z 1 – y = C
6.56 (a) 4 (b) Not exist. lim h 0 f 0, h = 2 / 3 lim h 0 f h, 0 = 3 / 2 (c) 8 2 (d) 0. xsin x 2 y 2 x 2 y 2 ∣ x ,as x 0 lim x 0 ; y 0 xsin x 2 y 2 x 2 y 2 0 (e) 0. lim x 0 ; y 1 1 x 2 y 1 2 =∞ ⇒ lim x 0 ; y 1 e 1 x 2 y 1 2 = 0 (f) Not exist . lim h 0 f h, 0 = lim h 0 2x x 2 =±∞ (g) 0. lim x 0 ; y 1 x y – 1 x – 1 – y = lim x 0 ; y 1 x  1 – y = 0 (h)1/3. Let z = xy 2 lim x 0 ; y 1 sin 1 xy 2 tan 1 3xy 6 = lim z 0 sin 1 z tan 1 3z , using L'Hospital rule, limit is 1/3. 6.58 Not exist. lim x 0 lim y 0 lim z 0 4 x y – 3 z 2 x – 5 y 2 z = lim x 0 lim y 0 4 x y 2 x – 5 y = lim x 0 4x 2x = 2 lim y 0 lim z 0 lim x 0 4 x y – 3 z 2 x – 5 y 2 z = lim y 0 lim z 0 y 3z 5y 2z = lim y 0 y 5y =− 1 / 5 6.62 (a) By definition. f

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HW4-510-soln - AMS 510 HW4 Solution 6.52(a x 2 y 2=C(b xy...

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