Applications Of Partial Derivative PDF

FACULTY OF ENGINEERING CE/IT/ELEC/BIO INFO. 01MA0106 – Calculus – Assignment - 5 ASSIGNMENT – 5 : Applications of Partial Derivative Do a...

FACULTY OF ENGINEERING CE/IT/ELEC/BIO INFO. 01MA0106 – Calculus – Assignment - 5 ASSIGNMENT – 5 : Applications of Partial Derivative Do as directed for the followings questions. 1 Find the equations of tangent plane and normal line at a point (3,4,5) to the Understanding surface 𝑥2 + 𝑦2 − 4𝑧 = 5 2 Find the equations of tangent plane and normal line at (1,2,3) on the surface Understanding 𝑥 2 + 𝑦 2 + 𝑧2 = 4 3 Find the equation of the tangent plane to the surface 𝑥2 + 2𝑦2 + 3𝑧2 = 12 at Understanding 1, 2, 1 4 Find the equations of tangent plane and normal line at the point  to Understanding the 𝑥2 + 2𝑦2 +3 𝑧2 = 12 5 Find the Jacobian of the following equation u=x siny v = y cosx Analysis 6 Find the Jacobian of the following equation u=xyz v= x2  y2  z2 , w = x+ y+ z Analysis 7 𝑥 𝑦 and 𝑥𝑦 Where 𝑥 𝑦 find Analysis 8 Find the maximum and minimum values of the function f (x, y)  2x  y onthe Analysis circle x2  y2  1 using the method of Lagrange multipliers. 9 The pressure P at any point  x, y, z in space is P  400xyz2.Find the highest Apply pressure on the surface of the unit sphere x  y  z  1. 2 2 2 10 Using Lagranges method of undetermined multipliers,find the maximum value Apply of x p yq zr ,when the variable x,y,z are subject to the condition ax  by  cz  p  q  r 1