Let flt.v) = v+3t°e'. -2 -y + 3t2e'. Then f satisfies a Lipschitz condition in y with L = 2, given that 1sts2. Select one: a. True b. False

Q: Hw. Determine t posdise red nd d. Sinx a x 2 In(X):07, de. os, Xa. 2, 3-tealion by e position fndla)…

A: NOTE:- By bartleby rules, only question (1) is answered

Q: (c(2z+y), %3D ue of c in the joi F of W.

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Q: Find Cマ×F ) マ if F (Miyız) 398 sin ni + COs C 8M - gy) t 10zK

A: Given : Fx,y,z = 8sinxi + cos8x-9yj+10zk

Q: Obtain the following Laplace ti 1) L{cos3t + 5e-t} 2) L{e¬3t (2t² – 5t + 1)} 3) L{sin7t – cosh3t} -

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Q: f(x) cos (at) if t 20 %3D 0 if t<0

A: Given: f(x)=cos αt if t≥0o if t&lt;0

Q: find dy ny the Chaenin Rult yz tan u and UzJxz+5

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Q: C. If w=f(x,y) and x = r. cose, y=r. sine. Prove that aw ar aw +1 (2001) = fx² + fy²

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Q: Prove that A <m AUB where AUB = {0x | r E A}U{ly|y € B}.

A: Solution: Let us consider two sets A and B. It may be possible that A∩B≠∅. But we want to construct…

Q: Compule he an Curvc given aM byO x= and ye 3tcos(t) 'from DLtL engh ot M pacbmeter 3t Sin (t)

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Q: šiven r,(t)=sin5ti +cos 5tj+\t+2k and r,(t)=5ti+2k , calculate "[r, (0) •r, (0)]. dt

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Q: given sin -In\x+ y + 19| Ax, y) = V18 – (x + 11)² – (y + 10)² sketch domain p(-11+ v7, - 10) is…

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Q: Find he value of ds /dy at u = 2 if s = t2 + 5t and t (u² + 2u)3 du %3D

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

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Q: QS A) Find IF y = - Ve IF y =-Vt and t sinx

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Q: (b) Show that, the function u = In(x² + y²) + 2 tan" satisfies Laplace's equation.

A: A Laplace equation is a 2nd-order partial differential equation. This is defined by,…

Q: dy Exercise: find O If y= Vu ua Sinx y= -Secu %3D

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Q: Assume sin(t) = - cot (-t) sec(t + 2) tan(t) = = = 3π 19 where π < t < ³. Compute the following: 20

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Q: Find ds/dt when u = 3pai/2 if s = cos u and du/dt = 5.

A: Given,

Q: If F = 2y i - zj + xk, evaluate Fx dr along the curve x = cos t, y = sin e, z = 2 cos t from t=0 to…

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Q: Express the curve by an equation in x and y given x(t) = sin(t) and y(t) = 8 + cos² (t). a) O-x² +y…

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Q: Be w = (u2 + v2)3/2, where u = e-t sin(θ), v = e-t cos(θ), calculate: ∂w/∂t and ∂w/∂θ

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Q: Let x,(t)-v(t)+sin(r), x,-vt) then x,(t)= xN-cosit) Select ones True, False

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Q: Consider the following position function. r(t) = (2 sin t,2 cos t) for 0sts 2x |v(t)| =]

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Q: If z = sin(rry). and * = t+ s, y = t2² + 8 8z when t=0, s=1. at Find

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Q: ди If u = e* siny where x = st? and y = s²t. Find ди and at as

A: Given data: The given function is u=exsiny. The second expression is x=st2. The third expression is…

Q: Consider curve C at R parameterized by: r(t) = cos(2t) î + tf+2 sin(2t)k, with 0 stsT An expression…

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Q: Let 0 be the angle between the line y = mx +band the x-axis. Prove thatm = tan 0.

A: The question should be :                 Let θ be the angle between the line y=mx+ b and the x-axis…

Q: Q1: - Find Ow/Du and Əw/Əv if w- xy + yz + xz ,x-utv, yru-v,z-uv at the point (u,v)- (0.5,1) (30…

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

Q: Use a local linear approximation of the function f(z) = VI cos[(V2r)] at some approximate v3.98…

A: To use local linear approximation of the below function to approximate 3.98cos7.963π. fx=xcos2x3π

Q: a²f If f(x,y) = e" sin (r + y), then prove that дхду дудх %3D

A: Hi! You have posted two non-related subparts. As nothing is specified, we are answering only the…

Q: Let / = x tan(x) dx. The approximation of I using the two-point Gaussian quadrature formula is:

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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: Given that f'(t) = 2sint + sec?t ,– t and f(0) = 4, find f(t) ドIN V V ドIN

A: Given, f'(t) = 2sint+sec2t  f(0) = 4 Formula used: Integral of sint = - cost Integral of sec2t =…

Q: 3) if y= CoSX then shift it by a) left TC b) Down1, lett 2

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Q: Q2:show that the force Fexyzi-x4z'k is Conservative. ?

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Q: 2. %3D be Centered in a batt co,ogo) andradies I 2. frove thet S-273R

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Q: Calculate us (t) * sin(t) using the definition of the convolution

A: Some of the Properties of Laplace transformation  Lsint=as2+a2Lu5(t)=e-5ssLf(t)*g(t)=Lf(t)·Lg(t)

Q: Utt || for 0 < x < T u(x, 0) = x? u:(x, 0) = }cos(8x) Uz(0, t) = u„(r, t) = 0

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Q: Find the function r that satisfies the given condition. r'(t) = (5, sin 8t, sec ct); r(0) = (3,3,3)…

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Q: 2- FIND f (t) or fis) AS APPRO PRIATE A) L}Je costdt COS ) y+2メ=8(t-)0)00)=イ

A: Here we use basic definition of Laplace transform

Q: 2, If fCx)=xInCx²+), find the ea uation for t4e tan9ent 1ine to fCx) at x= 3.Hint: Remember the…

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Q: Use an appropriate local linear approximation to estimate the value of co Gos(29°) &

A: consider   f(x) = cos x

Q: The acceleration of a truck is given by t2 +t a(t) = cm² / sec when 0<t<1. If v(0) = 1cm/sec, t +1…

A: Integrate

Q: If sint = - - and t is in the 3rd quadrant, then tan t %3D V45 45 O V45 V45 2 V53 O O O

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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: If f(z) = sin(z 2) = U(x, y) + iV (x, y), determine U and V . Verify that the C-R conditions are met…

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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: Find LT for f(t) = sin²(wt), f(t) = cos²(wt) %3D %3D

A: We need to find the Laplace transform of ft=sin2wt and ft=cos2wt Now, before finding the Laplace…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.