Thm. ①) [V₁ +V₂] 8 − [V₁]₂ + [V2]g ⑦ [av] 3 - α [V]₂ 2 3 V=O [v]8 ≤V=0 [V]₂ = 0

Son... LAIVI Find fr and fy for f(x, y) = (1 + x – 2y)e+2y Select one:

dx (hint: let x? – 2x + 5 = (2 – x)²) 7. J eVx² – 2x + 5 dx 8. (hint: let 2+x – p² = (1 + x)²z?) - J aV2+x – x²

x + 1 The integral - dx has a number of fractions equal to: x (x – 1)³ (2× + 1) Select one: а. 3 b. 5 С. 4 d. 2

EVALUATE Sx csc(2x) cot(2x) dx A. -zse (27) + la (ese (2) – cot (2-) + C B. z csc (2z) +In csc (2z) – cot (2x) +C C. -z cse (2r) - In (ese (2r) – cot (2) +C 1 D. rcsc (2z) -In (cse (2z) – cot (2r) + C

The function defined by y=Acos(In(x))+Bsin(In(x)) d²y dy +x dx is the solution of the following DE: x2- +y=0 - dx2 صواب İhi

Q.2 Use ODE methods to solve the PDE : U„-U̟ =5, U̟(x,0) = 3x², U(0, y) =0 ........

Evaluate ||/ (x + y – 52) dV where E E = {(x, y, z) | - 6 < y < 0,0 < x < y,0 < z < x + y²}

The degree of homogeneity of the function f(x, y) = (x² - 4y²)-¹/² O A. 1 B.-1 O C. -1/2 D. None of the Above O E. 1/2

Determine where the function f(x) = O A. (-∞, ∞) 1-00 O B. 3 3 OC. (-00²) U ( ²2.00) O D. 3 N/W 5x 2x - 3 is continuous.