Question

Find the tangent plane to the equation z = by cos(4x – 3y) at the point (3,4,24) Question Help: D Video

Answer 1

Solution ! finiy, z) = by 0 given surface is = 6y Cos (4u-34) We can write the - Z hafa by { cosyne coszy + osnym din zy} f = 6y. co synı coszy + by din ym. osin zy uz fa - Gy. Cosay (-yasinya) + syrahay Cycas yu) - o = -24y Coszy. Shya + 24 y sinzy. Cosun Now for the toplam In let ( 31412 = 29y. sin (zy -40) ay (4).csin (12. 12-12) 6 0 af ( 314, ay) fy- Cosqu (s. Cosytyt-sanu) - simen (5.wasy +67-360534) - fy = cosyn (6 cossy -18y din sy) + abinyu ( cosinsy roszy) = 6 Cosyn. Coszy - 18y Cosum-sinzy + 6 singu dinsy +18y sinyn. cossy 6 Cos (44-34) +184 sin (yn-3y) 11 +18 g 6 17 CS Scanned with CamScanner

2 fola (34.25 6. Coso +18 (4) sino lat ( 3, 4,24) 6.1 6. Sy latla at( 3,4, 24) 6 Again fz = -1 felar (24, 2n) - N where (Mor You to) - (3,4,34 Equation of the tangent Plane is fa (1o-do, ) (y- Mo) + f (Horder to -64-70) + (mode, 7)(z-7) 0 (4-3)+6 (9-4) -1 (z-ay) = 0 6 (4-4) - (<-ay) - by -24 -Z + 24 = 0 z = by is the equation of the tangent plane to the given surface at (3,4,24) 7 Ics Scanned with CamScanner