Find ∫C  ez / (z - πi) dz where C is defined as z(t) = 4eit and 0 ≤ t ≤ 2π.

Q: dy (b) Find ,where y = cos ecx –4 r +7 dx

A:

Q: Find the fay and fyy: f(x, y) = xe" - sin(xy) + x³y

A: fx,y=xey-sinxy+x3y

Q: ƏT ƏT and dr 3. Find of function T = x²y – xy³ + 2; x = r cos 0 and y=r sin 0

A: We have to find derivative

Q: 3. If G = (2x²y – x*)î + (e*y + y sin x)j+ (x² cos y)k, find: %3D дхду

A:

Q: "ind for f(x.y) = x sin(y+ 3z) fe dz

A: The solution is given below

Q: Suppose that r(t) =. Then the speed is

A:

Q: 4. Integrate the function f(z) = z² + 2z from z = -i to z = 1 in two ways, once along a straight…

A: The objective is to integrate the function fz=z¯2+2z from z=-i to z=1 in two ways, Once along the…

Q: Calculate for w-z sin(xy+).

A: The given function is w=zsinxy4+9z

Q: Let X: EXP(0). suppose Y= 2x , the Y is i = 1 Select one: a. Gamma (n,-) b. Camma(n. 4) С.…

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: 2. Differentiate. f(t) = et sin(2t)

A:

Q: The position of an object at time t is r(t) = (7 + t)i + e'j. Eliminate the parameter 1 to find y as…

A: Given the position of an object at time t is r ( t ) = ( 7 + t ) i + et j . We eliminate the…

Q: sin 4. Compute (1-7) dr. x(x−7)

A: (4)

Q: Evaluate r(2) and r(-1) for r(t) = (sin 1,12, (1² + 1)~1). %3D

A:

Q: B. Verify that dz/dy dz/dx 1 =. If xy + z = sinz.

A:

Q: Evaluate r(2) and r(-1) for r(t) =(sin~ t, t 2, (t2 + 1)- 1 ).

A: Given:rt=sint , t2, t2+1-1

Q: Let r(t) = . Find r′(t), and then find all values of t for which r(t) is smooth.

A:

Q: B ) if y= sinh¬1x then prove that =

A: Given y = sinh-1(x)sinh(y) = x On differentiating both sides , we get sinh(y)' = (x)'(cosh(y))dydx…

Q: Find the analytic function f(z) = u + iv if u = 2 cos x .cosh 2y cos 2x + cosh 2y

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Q: Identify a C? function f (x, y) with fx = x' + 4x?y and fy = 8xy – x'. (Enter DNE if no such…

A:

Q: ax B. (2y sinx – cos y) dx + (xsiny – 2cosx)dy = 0

A:

Q: wextan' (x *ャッ *ャッ

A: As per our guideline we are supposed to be answer only one question you can repost other questions…

Q: Sketch the graph of y = t + sin t for 0 ≤ t ≤ 2π.

A: The given function is y=t+sin t    for  0≤t≤2π. Sketch the graph of the above function as shown…

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.