Integrate the following three differentials over the three paths from (3/2,0) to (7/2,1) as shown in the figure below: dF = (5x² + 2xy)dx + 6y²dy dG = 2xdx + (3y² + x²)dy dH = dF + dG path 1 path 3 path 2

Q: 7. Find. V2x dx - 1

A:

Q: Find the cost function for the marginal cost function. 0.02x. C'(x) = 0.07 e fixed cost is $5 C(x) =

A: To solve the integral

Q: dx xVxt-8

A:

Q: Compute d (x+2) dxx-2,

A:

Q: dy If y = (5x + 1)(2x +In x), then will be %3D dx (5x + 1) +) + 5(2x+ In x) A. -1 B. (5x+ 1) - 2. +…

A: The given problem is to find the derivative of given function y=(5x+1)(2x-1+ln(x)) , we can use…

Q: 13. s = tan t – t

A: Solution: The objective is to find the derivative of the given function

Q: Find dy/dx if y = 3(x² − 2x)(6 + x5). O 21x6-36x5+ 36x - 36 21x6 + 36x5 + 36x - 36 O 21x6-36x5 + 36x…

A: Solve for the differentiation

Q: 8. (D2- 2D+ 1)y = xlnx

A:

Q: 2- Solve (4x + 2y + 3)dx - (6x + 3y – 2)dy = 0.

A:

Q: Find if y = (x² – 1) (x³ + 2). dx

A: We expand the given expression and then use power rule to find the derivative.

Q: dy Find of y = e4-3x + 63x*-2 x+5 dx

A: Given  y=e4-3x+63x4-2x+5 Find dydx

Q: 1/3 + 4y/6 = 2/3 Show your work

A: The given equation is 13+4y6=23To solve for the value of y

Q: (2e20 4e* – 1)ž 2 -

A:

Q: Find 9 dx

A:

Q: Find dy if x2 + 6xy = 3y2

A: Given: x2+6xy=3y2 If function if f(y) then differentiation w.r.t x is ddxf(y)=ddyf(y)dydx

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.