4, Q1 Q2 Q3 Q4 25 21 13 35 34 53 |3D %3D %3D %3D 2. 2. 4 Column A Column B 1. Whole number part of Q1 а. 1/2 2. Fraction part of Q2 · b. 6 3. Whole number part of Q3 C. 3/5 Whole number part of Q4 d. 8 5. Fraction part of Q5 e. 1-0

Q: 2e-u²+2 +2 dydz. 1

A: We have to evaluate the integral ∫01∫1u2e-u2+2dydz

Q: Determine |-5 (cot2 (4x + 7) + 1) dx.

A: Given∫-5cot2(4x+7)+1dxUsing identity :1+cot2x=csc2x=∫-5csc2(4x+7)dx

Q: f(3x² cot 2x³ csc 2x³) dx O-csc 2x³ + C CSC O csc 2x³ + C Ocsc 2x³ + C CSC O-csc 2x³ + C

A: We can solve as follows

Q: 1.25a +3> 0.5a-6 and 2.5a 129-1.5a

A:

Q: (5 – 6i) – (3 – 2i)

A: We have to perform the subtraction between two complex numbers.

Q: oB coser sec 2o -

A: To find the value of 2cosec20°sec20°

Q: Find x and y. x + 2 2 -7 2x + 6 2 -7 3 2y 2x 3 14 -8 5 -6 y +2 5 -6 9. (x, y) = %3D

A: Given data is  To find (x, y)

Q: 2p- dz 3.

A: We first factor the numerator and denominator to simplify

Q: 3.9b + a3 + 27 - 3a2 + 5a3 - 2a2 + 2.1b + 7

A:

Q: 3) %3D 2.

A: Two dimensional wave equation , by using separation of method

Q: 4 (2+ VT)5 5. Calculate 0.

A:

Q: 6y²dx- x(2x³ +y)dy = 0 a. x³yi = y#+ c b. x-3yi 2y+ c C. x³yi= yi+ c -y= 2y+ c d. x

A:

Q: 3. 2(2x2 + у?)dx — хуdy %3D0. |

A:

Q: (2 + j)?

A:

Q: Multiplt. 3i(4-i)

A:

Q: Simplify. (4y²– 2y-3)+(3y²–5y-4)-(8)²-4y-8)

A: Given :

Q: .2 y = 4 - x² and x +y = 2.

A:

Q: ..=A+B Ā +B al. B = 2ī + 2j - 2K 3Ā = -i- 3j- k US 1/

A: Given A¯ = -i¯-3j¯-k¯B¯ = 2i¯ +2j¯ -2k¯

Q: Solve for x and be sure to show Left side = Right side and Legal Moves. 7) Show all work. (Hint: Use…

A:

Q: aluate dx (2x+3)5 (2x+3)-4 + C -8 (2x+3)-4 + C 8 (2x+3)-5 + C -8 None

A:

Q: 8) Find BA -5 B = -7 -8 3 A = -6 6. 6 4. #7 #8 Is AB = BA ?

A:

Q: Find real numbers and such that 2.x – 3iy + 4ix – 2 y – 5–10ix = x + y – iy + 2-(3– x)i

A:

Q: Which edges shown on the graph to the right are not included in the following path? F. F. D. C, B, A…

A:

Q: [::], A = -1 3 3 B = C = 5 -2 -2 Compute A+B a) © 5B A + 5B O 2A + (38 - c)

A:

Q: 5. (-10, 1); 2r + 5y = 15 %3D

A: We have to calculate the equation of line at passing through a point (-10,1)  First we have to…

Q: b. 3+V5-x 3I

A:

Q: 3x + 5y = 4 3 (x, y) = %3D 4/3 %3D

A: We will solve the following equations as fellow:-

Q: y = x² + x y = x + 5 2

A: y=x2+x y=x+5   a2-b2=(a-b)(a+b)

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.