(A) Evaluate" [(x² + y)dx + (x + 1) 1+ along the path ABCA shown in figure C(0,3) A(0,1) x=3sint y=3cost

Q: 3 b) x² -3x+2 dx Sketch the graph! y

A: Given function is                                                          y=∫13x2-3x+2dx now…

Q: Tgir.y) = (2ry, 1+2+) and g(1.0)=8, then g(4.1)-9(2.1) =

A: Topic:- calculus

Q: 3 Find and sketch the graph of the domain of f (x, y)= 14x? +16у? - 64

A:

Q: (In æ)" Find y'. Let y = e" + 2

A: Explanation of the solution is given below...

Q: Find the Atend and matnix gF

A: Given a T be a linear transformation and Tx,y=x+y,y−x We have to find the standard matrix of T Let…

Q: XI. 6 F dF where F = (x³ – y, x + e') and C is triangle with vertices (0,0), (3,0), (4,2).

A:

Q: Evaluate 112 (2x - y) dx + (x + 8y) dy. C: x-axis from x = 0 to x = 2

A: To evaluate the given line integral

Q: Evaluate xy dx + (x+ y)dy along the.curve y = 4x from (- 3,36) to (- 2,16). C xy dx + (x + y)dy =] C…

A:

Q: Graph and shade the domain of f(x, y) = vy + x² – 2.

A:

Q: I. Evaluate the following: a. (x³ + cos y + 5 dy = - 3yx²) dx b. xdy – ydx = (4x2 + y2)dy c. dx +…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (3, -7) 21

A:

Q: 3 1-x Find [, [* (x³ + y)dydx

A:

Q: a z = 4x³-6x²y²-y com x= 2sen(t) y=-3cos(t) e

A: #As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Determine the NATURAL cubic spline S(x) that interpolates the data f (1) = 1, f (2) = 1, and f (3) =…

A: The given data  is x0=1 , x1=2 , x2=3 and fx0=1 , fx1=1 , fx2=0. The spline polynomial will consist…

Q: = Evaluate S₁2₁,22,23] f (2) dz where 21 = −i, z2 = 2 + 5i, zg 5i and f(x + y) = x² + iy

A:

Q: The graph of the function fCX)=x²+dx+q has only one X-intercept Select a valve for d that satifies…

A: For quadratic equation to be only one x-intercept , discriminant should be equal to zero.

Q: the diagram: ΔLMNΔLMN  is a right-angled triangle with vertices L(−6;7),M(a;b)L(−6;7),M(a;b) and…

A:

Q: 1. Find y if y =x In(4x+1).

A: Use the product rule of differentiation.

Q: Find Vf(a), given the following data. Calculate 91, 92 and g3 such that Vƒ(a): 91 92 93 = || || = 91…

A: The given problem is to find the grad f for the given data of directional derivative of function f…

Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (2, -7) 323 2

A: Here to find the value of line integral we consider two path c1 :from the point (0, 0) to (0, -7)…

Q: b) By using the given substitutions, show that i. Sx(x – 3)5dx =÷(x- 3)“(2x + 1) + C, z = x - 3 14…

A:

Q: 2 dy 67 +13

A:

Q: |(0,3) C1:x2 + y? = 9. (-3,0) C2 (3,0) Figure 1 Based on Figure 1 and given that F = y²i + (3xy +…

A: We have to find the work done by the vector force F =y2i+(3xy+4x)j Where c is a smooth circle…

Q: Let V be an F vector space of dimension n. Prove that, for k≤n the vectors V₁, V2, …, Vk are…

A: A set of vectors {v1,v2,...,vk} is linearly independent if the vector equation x1v1+x2v2+···+xkvk=0…

Q: Let a, ßeR ,such that 2(a -1)+ 3(a – 1)+ 6a=0 and 2(1-B)+ 3(1-B)-6B + 12=0 and a + B, also graph of…

A:

Q: 6. Find the x-intercept(s) of y= (x – 7) - 4

A:

Q: 1) Find whether the signals are memoryless or memory? a) y(t) = 5x2(t+2) b) w(t) = (t-9)x(t)

A: a) Given signal is: yt=5x2t+2 Substitute: t=1. y1=5x21+2y1=5x23 So, the output at t=1 depends upon…

Q: Find // (5x + y)dA where D : {(x, y) | x² + y? 0}

A:

Q: Determine the NATURAL cubic spline S(x) that interpolates the data f(1) = 1, ƒ(2) = 1, and f(3) = 0.

A: