Exercise 4 Given the double integral: 2 |e** dxdy. a) Make a figure showing the integration area of the double integral l in the xy plane. Use this to show that the integral can be rewritten as 2 x2 I = dydx. 0 0 b) Calculate the integral I. (Hint: (ex?) = 3x²ex®)

Q: Solve                 2   =   X-500/ 85

A: Firstly, we add 500/85 on both sides  and then by adding 2+500/85, we get the required result.

Q: Write the ratio as a ratio of whole numbers using fractional notation 12 to 1

A:

Q: Solve: 1/2x -3/5=2/5

A: We have given,

Q: 15x* – 30Ľ x +7L = 0 ² %3D

A:

Q: Solve : 3x2 - 4x = 4

A: Consider the given quadratic equation: Here the objective is to find the value of x.

Q: solution r^3 = 36r

A: The given equation is a third degree equation. So it has 3 solutions.

Q: X-X-30-0

A: x2 – x – 30 = 0Solve by completing the square.

Q: 3 + 4lnx =15

A: subtract both sides by 3

Q: Solve: 8*+5 = 4*-1 %3D

A:

Q: y" + 49y = 0 %3D

A: Given the differential equation y" + 49y = 0 The auxiliary equation is m2 + 49 = 0

Q: X^4-13x^2=-36 solve for x

A:

Q: Solve for x in the equation 3x² = 48 Ox=4 Ox= -4 Ox=4,-4 x = 4,8 Ox=2,8

A: Solution:

Q: 2x2 こ0

A:

Q: Solve the D. E. to the I. V. P. sinx(e-y + 1)x' – cosx = 1, y(0) = 0 %3D %3D (1 – e') (1 + cos.x) =…

A: We will find out the required solution.

Q: Solve for x: 6* = 35

A:

Q: 3x 9*-4x 27°

A:

Q: Differentiate - 3x 1 X+- X,

A:

Q: Solve: 2x + 5 = 3 or 2x + 3 < 3.

A: Given: 2x+5≥3 . 2x+3&lt;3 . When 2x+5≥3, 2x≥-2  x≥-1 When 2x+3&lt;3, 2x&lt;0  x&lt;0

Q: Solve: (1+5i)^3. O 110 - 74j O -74 - 110j O 74 + 110j O 110 + 74j

A:

Q: A cyclist bikes 20 kilometers in 2 hours. What is the cyclists pace in hours per 1 kilometer?

A:

Q: Solve: 4*1=162x-4

A:

Q: Solve : 2x2 = 250

A: 2x2=2502x

Q: Solve: 2x-gr+1 %3D

A: We use logarithmic properties to solve this equation