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- B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x %3D 4) y = ecosh(8x) ,5) y = t2 and x = V4t + 1 t2 + 1 x°cosx 6) y = Vtan?x, 7) y = ln |V1 + x2If f (x, y) = -Зу + sin (2x – 5y), then fyæ=? = xe -3e-3y – 10 sin (2x – 5y) –3e-3y + 10 cos (2x – 5y) 3e-3y + 10 sin (2x – 5y) O 3e-3y + 10 sin (2x – 5y)The equations xy² + 6xzcos(u) + ye" = 12 and x³yz + xe" 24 are %3D solved for u and v as functions of x, y and z near the point P where (x,y,z)=(1,1,1) and (u, v) = (5,0). Find () 2,y at P. u O -80,00 O 12,00 O -0,17 O 64,00 O - 30,00
- Calculate zu for z = 2x-y x+3y x = e2u ' cos(3v), y = e²u sin(3v)(5D' + 3D²)²y = 0 Select the correct response o y = (c1 + czt) cos 0.77t + (c3 + cst) sin 0.77t o y = C1 + Czt + (c3 + cst) cos 0.77t + (cs + cot) sin 0.77t O y = c1 + czt + Czť² + cst³ + (cz + cot) cos 0.77t + (c7 + cst) sin 0.77t O NoneFind the gradient of U = 2p(z² + 1) cos p. 2 cos ф (2?)а, +2 sin ф (z?)aф + 4pz cos ф a, 2 cos ф (z + 1)а, + 2 sin ф (z + 1)aф + 4pz cos ф аz 2 cos ф (z? + 1)a, + 2 sin ф (z? + 1)aф + 4pz cos ф а, 2 sin ф (z? + 1)a, + 2 cos ф (z? + 1)aф + 4pz cos ф аz
- 2) y(4) +xy(3) + x²y" – xy' + sin y = 0 Find the: Туре: Order: Linearity: Why?: Unknown Function: Independent Variable:If x*y' + xy' + (x? - +)v=0 x² - v=o x>0 ,V1=X 2 sinx , and y=y,v. Which of the following equations satisfied by v Select one: а. 1 3 (x Z sinx)v" + (2x cosx-x 2sinx +xZ sinx)v' = 0 2 sinx + x2 sinx)v' = 0 b. (x Zsinx)v" + (2x cosx)y=0 C. 1 (x 2 sinx)v" + (2x2 cosx)v' = 0 d. 1 Zsinx)v" + (2x (x cosx)v' = 0Find y' at the point (4, 4) where z sin(2² – y²) + 13 = – 3. Türkçe: z sin(z? – y?) + 13 = x² – 3 olmak üzere (4, 4) noktasında y' değerini hesaplayınız. 0,75 O -1,00 O -2,00 O 1,75 O 1,25 1,00 O 17,00 O 0,50
- 2 : Let F = (2x cos(x^2 + y^2), 2 + 2y cos(x^2 + y^2)) and C be the curve joining(-1,-1) to (-1,0) by traveling on the curves y = x^3 from (-1,-1) to (0,0), theny = x^2 from (0,0) to (1,1) and finally on y = − 1/4 (x + 1)(x − 3) from (1,1) to(-1,0). Evaluate∮C F · drz = sin(6x) sin(5y) az az dy IIasayfa O Yıldız Teknik Üniver.. When calculate the directional derivatives we of the function f(x,y,z)=x' + y* +z* _at the point (1,1,1) in different directions, which 4 of the following value(s) can we obtain? I:-8 II:-4 III :1 IV :5 V: 6 (a) I, II, Ш, IV, V (b) II, III, IV, V II, III, (с) 1, Ш, IV III, IV (d) II, III III, IV (e) Only II III ly II