4. Find the general solution to each of the following differential equations. (a) 2xy² - 1 + [cos(y)+2x²y] dy dx = 0. dy (b) 2xy - cos(x) + x²- = 0. dx

Q: In ( x² + 3x -=-7) dx X-2 Evaluate the integral: Se Ⓒ + A x² 2 =+ + In|3x-6|+C ℗ +² +5x+3n|x-2/+C B…

A: To find out the integration.

Q: lim (x-7) tan x x→2 플

A: The objective is to evaluate the limit.

Q: Determine the general parametric solution of the following unsolved differential equations for the…

A: See the details solution in below

Q: (D³ - 5D + 4)y = 0, when x = 0, y = -2, y' = 8, y" = 0

A: The given differential equation is: D3-5D+4y=0 when x=0, y=-2, y'=8, y''=0.

Q: Find the area bounded by x2 = 4y + 4 and x = y = 2. Using vertical element, what is the integral…

A:

Q: 02/Use the l'Hopital's rule to find the limits in t3-4t+15 a) lim t--3 t²-t-12 X-8x² X-00 12x²+5x b)…

A: Given problem:-

Q: Given f(x)=4x+1 and g(x)= x²+x-3: Use the disk method to determine the volume of solid obtained by…

A:

Q: Find the area bounded by : f(x)=e*, g(x)=e¯* and x=3. A (e²+ 1)² e² sq. units B (e³+ 1)² e3 (e³-1)²…

A: Given that,

Q: Find the linear equation of the given below using any of the 3 methods. Show your solutions here. X…

A:

Q: Numerical Integration: 5 (2x² – 3x) dx 2. 2

A:

Q: (a) Find the point of intersection of the tangent lines to the curve r(t) = (2 sin(at), 3 sin(at), 5…

A: We have to find equation of tangent.

Q: To reduce the DE (x+2y-4)dx-(2x+y-5)dy=0 to a DE with homogeneous coefficients, use the…

A: solution:-x+2y-4dx-2x+y-5dy=0dydx=x+2y-42x+y-5the system of linear equation…

Q: Integrate the equation using the method in trigonometric substition

A:

Q: 1. Solve for x and y in xy + 8 + j(x2y + y) = 4x + 4 + j(xy² + x) A. 2, 2, B. 2,3 C. 3,2 2.…

A: We can find the values of x and y. Note :As per our Guidelines , we can solve first question…

Q: Question 7 In evaluating 4 2 dx X√√x²-4 s-¹(f(x)). Determine the value of f(x) if x=0.35 is same as…

A:

Q: Integrate the equation using the method in trigonometric

A:

Q: If y = arcsin (e5e), Check Answer dy da

A:

Q: Find the equation(s) of a line that is tangent to f(x) =4x - x² and pass through P (2,5). (Provide…

A:

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)= x + 1 3 A 2-unit² 1 Ⓡ / unit²…

A:

Q: Lim X-0 √1+x-√1-x x

A: evaluate the limit limx→01+x-1-xx

Q: A metal sphere cools from 60°C to 50°C in 5 minutes. How much more time (in minutes) will it take to…

A:

Q: Which of the following CANNOT be solved by method of undetermined coefficients? 1 A (D²+1)y=. cos x…

A:

Q: Given A B U D ₁₁f(x) dx = 0 and 0 1 f²³f(x) 11 6 11 55 6 f(x) dx = 11 6 * evaluate ,0 √3f(x) dx -…

A:

Q: H.W // find the integral _1=√15 e-x³².dx. using 7. dx. using two and three points of Gaussian -1.5…

A: In numerical analysis, the Gaussian Quadrature method approximates the definite integral of a…

Q: The given function v = ln (xy) + ex+y Determine Ov/ox

A:

Q: 3. Look at the figure below. Find the value of x and the measure of each angle. n 1.x = 2.42 = 3.26…

A: We know that alternative interior angles are same Therefore 5x-14=3x+18 Subtract 3x+18 from both…

Q: 12. Find the first and second derivatives of f (x) at x = 1.2 and x=2.0 from the following table 1.2…

A:

Q: What is the value of C if r(π/3)=2? * O 2 0 TT/2 none of the choices

A:

Q: Lim (112²28 - 1²/²) \sin²x

A: Given problem:-

Q: Given than f(x) dx = 4 and A None of the given choices ℗ 25 (2) dx = [1 (2) de B f(x) © f (x) dx =…

A:

Q: The hyperbolic paraboloid (saddle) f(x, y) = x² - y² + 4 is shown in the 3D model below. Find the…

A: Here, to find the volume f(x,y)=x2-y2+4 between the rectangle R=[-2,4]×[-1,2]

Q: Q3/Find a volume for the region bounded by 4/X and Y = (X-3)² about the x-axis.

A:

Q: 29. A body temperature of 50°F is placed outdoor where the temperature is 100°F. If after 5 minutes…

A: As per our norms we have to write one question at a time kindly repost remaining questions

Q: For questions no. 4 and 5. Given: Radium decomposed at a rate proportional to the quality of radium…

A:

Q: a + bx² 3ax + bx³ dx

A:

Q: efv. Evaluate dx Use rationalizing substitution. A B 8 √e² - 2 - 2√2 Arctan — √e² - 2 + C e³ − 2 −…

A: Let's evaluate given integral by using rationalizing substitution.

Q: 2. Simple Chemical Conversion Radium decomposed at a rate proportional to the quality of radium…

A: This is a problem related to decay law. Based on the general formula and concept we will answer the…

Q: y" - 3y' + 2y = 6

A:

Q: when the first nine terms of an arithmetic sequence is added. its sum is 72. what is the value of…

A: The fifth term will be ,a5=a+4d=8

Q: وم .dx I+ V !+ v x

A: Solve

Q: 3 [²(x²) dx 0 Using the definition of definite integral, ff(x)dx= lim f(x) Ax, and the given…

A: Given, ∫03x2dx

Q: Find 4-¹, if A = [3 3 O ] 3 -2 0 O [32] −3 0 - [²2] O −3 12 -=[ 132] -3-2 O 2 3 3 2

A:

Q: S dx secx + 1 Transforming Ⓒ / + A -dz 1+z² 2-2z² (B) 1+z² C 12²+2 dz Ⓒ √ 1+2²2 dz D 1-z² -dz using…

A:

Q: 1. f In(x+2) dx 2x+4 2. fx² ex dx 3. f tan³x dx 12

A: We know that integration of xn is xn+1 /n+1. And integration of 1/x is lnx +c.   Here i attached the…

Q: 6. Determine the area of the region bounded by x = −y²+ 10 and x = (y 2)²

A:

Q: 4. Use the washer method to determine the volume of the solid obtained by the revolving the region…

A:

Q: .b if f is continuous on [a,b], and f(x) 20 then √VF(x) dx = f(x) dx T True F False

A: Topic: application of integration

Q: For questions no. 2 and 3. Given: A thermometer reading is 60°F at 3:00AM and a Civil Engineering…

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: Question 32 dx Evaluate: (x+1) log(x+1) A) -In 10 log2 (x+1) + C 2 B --log² (x+1)+C 2 In 10…

A:

Q: Question 1 A body cools from 60°C to 50°C in 5 minutes. How much more time (in minutes) will it take…

A: