Question

Question 1 < Find the tangent plane to the equation z = 3.12 2y2 + 3y at the point (-4, -3, - 75) 2 Question 2 Find the tangent plane to the equation z = 5ex°-by at the point (12, 24, 5) Question 3 < > Find the tangent plane to the equation z = 5y cos(3x – 2y) at the point (2,3,15) z = Question 4 at the point (4,2,8), and use it to Find the linear approximation to the equation f(x, y) = 4, approximate f(4.28, 2.24) /(4.28, 2.24) Make sure your answer is accurate to at least three decimal places, or give an exact answer. Question + 5 Find given: dt x = te2v, z = tô, x = 5+ 6t dt Your answer should only involve the variablet Question 26 < Given f(x, y) = sin(x + y) where x = søt, y = 6s - 2t. Find f.(x(s, t), y(s, t)) - f. (c(s, t), y(s, t)) = Note: This question is looking for the answer to be only in terms of s and t

Answer 1

2. equation of tangent plane of F(x, y, z)= 0 at (12,24,5). ore + 3o e Fax (12,24,5)(x-12)+ fy (12,24,5) (7-24) +&g (12,24,5) (2-5) = 0 12² – 6.24 -10.12.0 12?_ 6.24 (9-24) + z-5=0 on, - 120 e® (x-128) + 30 °(4-24)+2 50 --1202 + 1440 + 30 Y - 720 +2-520 - 1200 + 200 az + 715=0 z : 120x - 304 - 715 on, 3. Find 1 the tangent plane to the equation 2=5505 (3x-2y) out the point (2x3, 15) So F(2,4,7 )=25 y ens (33~24) Fxe CX, 312)=-59 ha ( sin (3x-2y) - 3 = 6159 Sim (32-20) Fy (X,Y,Z) =-510S ( 3x-29) #5 y sin (3x-2y)•(-2) Eng OS ( 3x-2m) #10y sin( 3x-20) Ez (*19,2)=1 equation of tangent plane 15.3.sin(6-6) (x-2)-(520s (66) - soy sin(6-7 (-3) + 11(7-15): or 0.(x-2) - (5-7)(y-3) + 7-1550 - 5y + 15 + z-15=0 z = sy. on, page-2

4. 5. Find d2 at given : 2 = xe х = +3, y = 5 + + + 29 d2 • 2 » x. + хе d? + oxe29 см dt 4м) 3+2 dt de 19. 24°, хе, с e 22 t 12 Хе 3t?е? 9 х = t2, (34° 12% ) 29. = (34°, 12. 13) е 2 (5+6+) (ронеж 34? ( 1+1+) е 16 +10+. 2 (5+6+) te 2 - хе otherwise (o t 124 х2) 12104 124 312 сто+12+ + + 3 с 2 dt - 4* (244) est t24. Gautrew 3 X=uW?ws ° +y) 1. 2 09) 2 ЭХ зи ас Әи Х әа - 2 ги 9cc 2 да 2. 99+ х 3 - 2 (uv°, 5) v? + v?. ( u ve“) 21 з'uv", ") tu ve). 2(+02:4+ 9: + 3. 1) with) + 2 (+) (321- - 12 +576 4 0 432 = 1, 17 22 әUA Lal, N: 3 - о Протез

6. f (x, ) = sin(x+1), x=s$+”, Y=65-27 fs = 2t әS f(x,y) = sin(st² +65-2+) ins (3642485-24).(estac:1) = 6/55 +²+1) cos(564²+63-24) cas (g€'+65-24) (562t - 2.1) = 9 (set-1) cos(sft+65-2+) ft = of 11 (pase. 4)