Establish: Use: cos (Z) = e² eiz + e-iz 2 a lo Zn n!

Q: Compute r"(t) when r(t) = ⟨t10, 8t, cos t⟩ .

A: Given:

Q: The integer n = 12700140x3243243 is missing the digit x. a) If n congruent to  3 (mod 9), then what…

A: According to the given information, Consider the given integer n:

Q: Given z = g(x,y) = ln(y) . cos(2x - 3y), show 02g -(x, y) дудх 02g - (x, y) : дхду =

A:

Q: (d) Find E[XY]. (e) Find Cov(X,Y) and Corr(X, Y).

A: The bivariate distribution of two variable X and Y are given

Q: Find the Integration of 1 dx. (6x+7)6

A: To find: The integral of ∫dx6x+76. Formula used: Integration formula: Power rule of integration:…

Q: Verify that the function u, defined by u(t, x) = t sin(x – t²), is a solution to the equation ,2 U +…

A:

Q: d?y taby = Fo cos ot, where wo, ware positive con- dt- stants, and Fo is an arbitrary constant. You…

A: Given differential equation, d2ydt2+ω02y=F0cosωt      ...(1)

Q: Find cos (x² + y²)dA where D = {(x, y) | 9 ≤ x² + y² ≤ 36 Round your answer to four decimal places.

A:

Q: (b) Ir(t) x u(t)] dt (i) Find the product first, then differentiate. (ii) Apply the properties of…

A:

Q: Use the substitution z = e to turn t'a eciation below into a linear equation in z: dy =…

A: Given differential equation .We have to linearizing the differential equation using

Q: Use the equation to find dy dx }} dy dx dy dx ƏF ƏF ду = F X F y 7y cos(x) = x2 + y2

A:

Q: By substitution, z=ln(x), the equation, x2y''+2y=0, will be transformed to an equation in the form…

A:

Q: (i) Find fæ, fy, fry, far and fyy for the function: f(x, y) = e¹y² + x³y³ . Verify that fry = fyx.…

A:

Q: Use the tangent equation. tollowing equation to find the approximation at Co,0): fCX.y)e Jy+ cos cx)…

A: The given function is: f(x,y)=y+cos2x

Q: Exercise 1. A student is asked to prove If m is even and n is odd, then m² + n² is odd. 2 The…

A: Let us answer above questions

Q: Evaluate the convolution, f(t) * g(t) = e®t * sin (t), then evaluate at t = 1.

A: Solution: