logo

Engineering Mathematics - Doc

10 Pages457 Words69 Views
   

Added on  2020-04-21

Engineering Mathematics - Doc

   Added on 2020-04-21

ShareRelated Documents
Running head: ENGINEERING MATHEMATICS1Engineering MathematicsNameInstitution11234567891011
Engineering Mathematics - Doc_1
ENGINEERING MATHEMATICS2Question 1∇f1=(∂f1∂x^x+∂f1∂y^y+∂f1∂z^z)∂f1∂x=128xyyln(128)−3sin⁡(x)∂f1∂y=128xyxln(128)∂f1∂z=3∇f1=(128¿¿xyyln(128),−3sin(x)),128xyxln(128)+3¿∇f1at (8, -1,36) = (-3sin (8) +72057594037927936ln (128))^x+(576460752303423488ln (128))^y+3^z)Question 2θρ∅∇f2=(∂f2∂ρ^ρ+∂f2ρ∂∅^∅+∂f2∂z^z)∂f2∂ρ^ρ=¿-5z2¿^ρ∂f2∂ρ^ρat (1, 7/6, 12) =24−93.5307−720=−789.5307^ρ∂f2ρ∂∅^∅=−9zsin(∅)^∅∂f2ρ∂∅^∅ at (1, 7/6, 12)¿−9(12)sin(7π6)=54^∅∂f2∂z^z=(9ρcos(∅)−10zρ)^z∂f2∂z^z at (1, 7/6, 12) =9(1)cos(7π6)−10(12)(1)=−127.794^z∇f2=−789.5307^ρ+54^∅−127.794^zQuestion 3Evaluate f3 at (45, 1/4, 1/3)1213141516171819202122232425262728293031
Engineering Mathematics - Doc_2
ENGINEERING MATHEMATICS3∇f3=(∂f3∂r^r+∂f3r∂θ^θ+∂f3rsin(θ)∂∅^∅)∂f3∂r^r=24r2sin∅cosθ−4sin2(∅)∂f3∂r^rat point (45, 1/4, 1/3)¿24(452)sin(π3)cos(π4)−4sin2(π3)=29758.3^r∂f3r∂θ^θ=1r(−8r3sin∅sinθ)=(−8r2sin∅sinθ)∂f3r∂θ^θat point (45, 1/4, 1/3)¿−8(45)2sin(π3)sin(π4)=−9920.433^θ∂f3rsin(θ)∂∅^∅=1rsinθ(8r3cos∅cosθ−4rsin(2∅))∂f3rsin(θ)∂∅^∅ at point (45, 1/4, 1/3)¿145sin(π4)¿∇f3=29758.3^r−9920.433^θ+7944.115^∅Question 4Evaluate G1 at (4, 7, 1).∇.G1=(∂G1∂x+∂G1∂y+∂G1∂z)∂G1∂x=8xy∂G1∂y=5xz2∂G1∂z=0∇.G1=8xy+5xz2+0=8(4×7)+5(4×1)=244Question 5Evaluate G2 at (4, 4/2, 7).323334353637383940414243444546474849
Engineering Mathematics - Doc_3

End of preview

Want to access all the pages? Upload your documents or become a member.

Related Documents
Engineering Mathematics 1
|11
|1704
|136

Assignment on Numerical Methods
|7
|835
|361

Mathematical Skills for Software Engineers, Quadratic Expressions, Vectors and Matrices
|27
|2733
|195