Let z=xin(x2+y²-eª)-162xy, x=te°, y=et. If the value of when s=2 and t=1 is equal to Ae?+Be", then A+B=

Q: Suppose z = x + 2i and u= 3+ yi where x, y E R. Find the smallest positive value of x z + u for…

A: Substituting z=x+2i and u=3+yi in z+uz-u:  z+uz-u=x+2i+3+yix+2i-3+yi           =x+3+2+yix-3+2-yi

Q: Let c (t) = (e", sin(-21), t'), and c2 (t) = (e", cos(t), -t) d [c (t) c2 (t)] = [C (t) x c2 (t)] =…

A: To find d/dt(c1(t).c(t)) d/dt(c1(t)*c2(t))

Q: (c) x(t) = eat cos s wtu(t), a > 0 (d) x(t) = e-af sin w,tu(t), a > 0 %3D

A: Let xt is a function. The Fourier transform of the function xt is denoted by Xiwor Xf and defined by…

Q: 19.Show that W[eλt cos(μt), eλt sin(μt)] = μe2λt.

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Q: 10. y = C, cos 4x + C2 sin 4x + C3xcos 4x + C4xsin x + C5; C, to C5 are arbitrary constants

A: Since their are 5 arbitrary constants so the differential Equations will be of order 5. We find the…

Q: If z= r +y, I= e' cos(s) and y= e' sin(s), then %3D 8z as at (t, s) = (1,0) is O-2e O 4e O 2e? 2e

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Q: (2) = [| (a) %3D h (b) Value(s) that are NOT in the domain of -

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Q: If r(t) = (V10 – t, In(t – 1), sin(2t)) - then the domain of r is О 11, 10] (1, 0) O [1, 10) O…

A: Explanation of the answer is as follows

Q: 52. If z = f (x, y), where x = r cos 0 and y = r sin 0, find a. Əz/Ər, b. дz/80, and c. d z/Ər d0.

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Q: If r (t) = (sin(t), cos(t), 2), then ſr (t) dt = 0.

A: The vector function is given by rt = sin(t),cos(t),2 To evaluate : ∫0πrtdt

Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (b) z = x2 + 3xy + y2 ; x = sin s + cos t, y = sin s - cos t

A: Consider z=fx,y & x=fs,t, y=fs,t Then, the derivative of z with respect to s is given by:…

Q: The functions y,(t) = sin(2t), y,(t)= cos(2t) are linearly independent on (-0, x). Select one: OTrue…

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Q: Find i (t), given 7(t) = (5 cos(– 2t + 3), 4te', – 2t In( – t)). %3D F (t) =

A: To find the derivative of the given parametric vector, we need to differentiate each component of…

Q: If u = x¹y + y²z³, where x = rse, y = rs²e-t and z = r²s sint, find the value of Ou/Os and Əu/ər…

A: According to the guidelines, we are answering first question. Please repost the remaining.…

Q: For z C, show that the solutions of cosh(z) = 1 are z= i2km, for ke Z.

A: We need to prove that the solutions of the equation: cosh(z)=1 are z=i2kπ, where z∈ℂ, k∈ℤ.

Q: π/3 So, f²ef/³ t In u tans ds du dt

A: Given problem:-

Q: 18 Compute r''(t) when r(t) = (t°,9t, cos t). r'(t) = OID

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Q: Find e + Uy, Given that u(x,y) tan(x+11Xy+11y") .t/ - *א- w

A: Given ux,y=tanx+11x2y2+11y411-x2-y2

Q: Find the value of ds/du at u = 2 if s = t^2 + 5t and t = (u2 + 2u)^(1/3).

A: Find ds/dt from s=t^2+5t

Q: Q3 Suppose that w = x² + y² + z² x = e" cos 0 ,y= e"sin0 ,z = re® aw аnd ar aw Find дө

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Q: Let z x = 2 cos u, and y 3 sin v. Find dz in terms of u and v. %3D Provide your answer below:

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Q: if z sin とこ3r'+25 , Y=4イ-ス3 Z = 2r-35* W= Z Sin %3D * find aw,w ar me' me as

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Q: et sin t? blas Y - et cos t? lio -n/2 <t < 0

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Q: d) sin[w,(t-1)] u(t)

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Q: T/2 T (² cos 2y + 3y° sin z) dz dy . Evaluate -1/2 Jo

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Q: If r(t) = (V10 – t, In(t – 1), sin(2t)) , then the domain of r is

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Q: N 1 1 202 2{(xn – µ)²}– z(Ord – r). n=1

A: Let y be a function of x and if a is a constant, then we know that ddx(a-x)2= -2(a-x). Here, we need…

Q: əz Əz Əx Əy Q5-A) If z =(x +by)² +e+by+sin( ax +by) show that b =a

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Q: If r (t) = (cos(t), sin(t), 2) , then fr (t) dt %3D

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Q: 1. r(t) = ti + (In cos t)j, -T/2 < t < T/2

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: a) Find dz, if z = e' sin e %3D b) Verify uxy = uyx , if u = In /x² + y² . %3D

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Given f(x,y) = ex cos y, Evaluate fx(2,0) A cos 2 B) sin 2 C) 0 D) e²

A: fx is the partial derivative w.r.t. x

Q: Given that r = 3 cos nt, y = 3 sin at and z 4nt with 0<t <1. Evaluate (x+ 2) ds.

A: The line integral is defined as,

Q: If r (t) = (cos(t), sin(t), 2) , then ſr (t) dt =

A: r(t)=&lt; cos(t), sin(t) ,2&gt;

Q: (b) Determine whether u(x,t)= e' sinx is a solution to L

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Q: Let z=xln(x2+y2-e4)-161xy, x=te, y=est. If the value of 2 when s=2 and t=1 is equal to Ae2+Be“, then…

A: From the chain rule, ∂z∂t=∂z∂x×∂x∂t+∂z∂y×∂y∂t Now,…

Q: Given that u(t) = (e",5,cos 5t) and v(t) = (3,sin 41,4). Find [u(1) v()]. dt

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Q: Let r(t) = (sin 3r, cos 3r, /īt), Find T(t) and N(t)

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Q: Given f(x.y) = e X cos y, Evaluate fx(2,0) e2 cos 2 O sin 2

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Q: f(t) = et+1 cos t. f(t) = eat43/2_ f(t) = eat cos 3t.

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Q: If u = x3 + y3 where x = a cos t, y = b sin t, then du dt

A: Solution

Q: If r (t) = (sin(t), cos(t), 2). then ſr (t) dt =

A: we have to find the following

Q: Given z 15 In(t) and y= 225 t then find dy da dy dr?

A: Given that: x=15ln ty=225 t2

Q: 9. Jer'y ds, C:x cos t, y sin 1, z = 1, 0<1s/2 %3D 77

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Q: dz az If z = xyeX/Y, x = r cos(0), and y = r sin(0), find and ar when r = 2 and 0 = %3D az ar (r, 0)…

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Q: So Evaluate F. dr where C F = (– 2z, – y, – 4x), and C is given by 7(t) = (sin(t), cos(t), t), 0 < t…

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Q: (T/2 Q = [" 3 sin t(cos t)?dt

A: Given,        Q=∫0π23sintcost2dt

Q: Find C if r(t) = ⟨et, 3 cos t, t + 10⟩ + C and r(0) = ⟨0, 0, 0⟩.

A: We have given function r(t)   r(t) = ⟨et, 3 cos t, t+10⟩ +C   We have to find the value of C   It…

Q: f : [o,s] → A? flt) = ( 6E) 2 cosh 3t, - 2 sin 3t, Compute f'lt).

A: If f(t) is differentiated with respect to t, then f'(t) is obtained. Let f(t)=x(t), y(t), z(t), then…

Q: A) Let w = 4x2 +4y² + z?, x = p sin o cos e, y = p sin o sin 0, z = pcos o. Find aw/ap, aw/a6, and…

A: "Since you asked multiple questions we will solve the first question for you. To get any specific…