3. In each case, find the order m of the pole and the corresponding residue B at the singularity z = 0: (a) sinh z z4 1 (b) z(e² - 1) Ans. (a) m = 3, B = 6' (b) m2, B=- Find the value of th

Q: Find the following for the given equation. r(t) = (e-t, 5t², 7 tan(t)) (a) r(t) (b) r"(t) = (c) Find…

A: Given: rt = e-t, 5t2, 7 tan t To find: r't , r''t and r'(t)·r''t We know that  ddxex = ex ; ddxtanx…

Q: Consider the function h (t) = e-3t cos (2t) . Compute h' (7/3) - Number FORMATTING: Give the value…

A: In the given question, concept of derivative is applied. Derivative The derivative expresses the…

Q: 2. Which of the following functions is of exponential order? * 4 f(t)= Sin 4t f(t)= 5{VT + A.) O B.)…

A: The function of exponential order is determined as shown below.

Q: Write a in the form a = a-T+ anN at the given value of t without finding T and N. r(t) = (6 e'V5) i+…

A:

Q: Find the derivative of sinh(x)tanh(x).

A: As per our guidelines I am solving only first problem please repost other question.  y = sinh(x).…

Q: Find a harmonic conjugate of the function u(x, y) = arctan(x/y)− 6

A: Solution :-

Q: Find T, N and B for the curve 7(t) = (4 cos(2t), 4 sin(2t), 2t) at the point t = 0 %3D Give your…

A: given that                                          r→(t)=4cos(2t), 4sin(2t), 2t at t=0…

Q: A particle is moving along the path given by R(t) = (sin(ln t), cos(ln t), √√3 lnt). (a)…

A: Introduction: The formula of arc-length of the polar curve from a to b is given by,…

Q: Find the tangent line to the curve x cos y + y cos x = 1 at (0,1). O A. (cos 1)æ + y = 1 O B. x + y…

A: We can find the tangent line as below

Q: Find the length L of the curve R(t) = e" cos(2t) i + e* sin(2t) j+2e"k over the interval [1, 4]. L =

A:

Q: Find the arc length of the curve c(t) = (5 cos(t), 5 sin(t), -13t) on the interval 0 ≤ t ≤ 2.…

A:

Q: determine the value of k which will make h' (π/4)=6 when h(x)=In(cosx)+kx. a. 6 b. 5 c. 0 d. 7

A: Given, hx=lncosx+kx We have to find the value of k for which h'π4=6

Q: Let f(t) = 2 cost – 1 and g(t) = 3at. (a) Find (fo g)(t).

A: Given  f(t)=2 cos t -1g(t)=3πt Find fog(t)=fg(t)

Q: 2. Find L .2 t2 sin(2@t) F(t) = А. %3D 20 sin(@³r) F(t) = В. 2ot t sin(@t) С. F(t) =- %3D 20 cos(@t)…

A: The given function is Fs=ss2+ω22 We have to find the inverse Laplace transform of F(s). To find this…

Q: 6a) Let A be the parabolic arc defined by the equation y = 8x – x´ over the domain interval [0, 8].…

A: (a) Consider the given function. y=8x-x2 Now, draw the above function by using the calculator.

Q: Find the arc length of the curve c(t) = (cos(9t), sin(9t), 2t³/2) on the interval 0 ≤ t ≤ 1.…

A:

Q: Write a in the form a = a-T+ anN at the given value of t without finding T and N. r(t) = (5 e' cos…

A:

Q: Find f. f(t) = 5e¹ - 6 sin(t) — 5 f"(t) = 5et + 6 sin t, f(0) = 0, f(π) = X 0

A:

Q: Find the domain of the vector function 7(t) = Domain: {t| <t< }

A:

Q: a. Show that If z = x+ iy where y 1 b. Evaluate: cosh?(-z) – sinh²(z)

A: Given that z =x+iy For a part , y&lt;0 and we need to prove that | eiz | &gt;1 For b part, we need…

Q: particle moves such that its velocity at time t is r(t) = (3 cos nt, 2 sin nt, t) and such that it…

A:

Q: Let z be defined implicitly as a function of x and y by the equation dz 4+ In (xy²) – cos (xy – z) =…

A: