HW.8. Use farseval's theorem to find if f(t)=A e-alti Ans: A?

Q: If a is a positive integer, then the slope of the tangent to the graph of y = a²x – a ln(ax +1) at z…

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Q: 20) Let y=7x+5x Then compute dy and Ay for X= -7 and dx =0.4. dy =? and Ay = ? Gounded 6o 4 decimal…

A: Derivative: - The derivative of the function is the equation that we find. The instantaneous rate of…

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

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Q: Compute the length of the curve over the given interval. r(t) =〈2t, ln t,t^2〉, 1 ≤ t ≤ 4

A: it is known that the length of the curve can be calcualted by the integral formula…

Q: ! = 0.25y² is to (implicit) Euler's condition y = 1 at What would be th

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Q: in term of t, if w -+, x= cos t,y sint and z in term of t. if w = xy, x = cost and y = sint, whent=.…

A: 4. Given data is : w=xz+yz , x=cos2t , y=sin2t  and z=1t To express dwdt in terms of t

Q: (a) if f (t) = te“ cos 5t then L{f (t)} =?. %3D 4s2 + 19s + 52 (b) if F (s) then L-1{F(s)}=? %3D s…

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Q: ON REDMI Y3 AL CAMERA - veifhy coucly's is Theorem for the function C) 3 Cosh(z+2 where C is the…

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Q: Q2: find dw/dt at given value point for the following function 1) w =x +y.x= cos(t). y = sin(t), at…

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Q: (Note: This is a f(x) of Hyperbolic) e¯* + e* dx о ех — е х

A: We have to solve

Q: Q1. If f(x.y,z) = cosh²(\x² In y) + tan-(ey*NE) + sec*(sin Vz In x²) Find fx, fy, fz fyx

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Q: 1 use the formula L = dt to find the length of the curve dt dt 1 X = y = t° for 0st s1

A: according to the guideline, we are allowed to answer the only the first question  please repost…

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: Consider the following. f(s, t) = s In(7t) + e-1.33t f(s, t) = 2 for 1sts 20 tangent line at t = 10…

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Q: Find the following F(s) = t² e=st dt s > 0

A: The Laplace transform of a function ft is given by Fs=Lft=∫0∞fte-stdt, where Fs is a Laplace…

Q: COS Z fined the Res of the function T Z 4 -

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Q: - If x=sect and y = tan t, evaluate at t of the following: 4. dy (a) dx d y (b) dx?

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Q: 4. If u = xy + y²z³, where x = rset, y = rs²e-t and z = r²s sint, find the value of du/ds and au/ar…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: /hich of the following does not require the use of the dy nain rule to find ? dx A y = cos1 (10x –…

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Q: Q: IF the value of (t) change from sin(“,) to cos( ",5. Find the dF for dx f(x, t) = V1+t³ Sa f(x,t)…

A: To find dFdx, whereF=∫αxβxfx,tdt, and fx,t=1+t3

Q: Given F(2) = 1, F'(2) = 1, F(3) = 4, F'(3) find each of the following. (Enter dne for any derivative…

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Q: If r = sin ( ƒ(t)), ƒ(0) = p/3, and ƒ'(0) = 4, then what is dr/dt at t = 0?

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Q: 8. Find the length of the given curve over the indicated interval. r(t)= (r', 3 cos(t), 3t) [] 0, 2

A: Given r¯(t)=t2,3cost,3t in the interval [0,π2]

Q: Obtain dy from the following function y=e'

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Q: 15. Find the equation of the tangent line to the curve at point (0, In 2). y = In(e' + e4) O 2y + 5x…

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Q: 1. Differentiate the following: G(t) = sinh(In t) %3D G (t) = ? a. Cosh 3t b. y = ?

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Q: For the functions w = 8x + 3y, x= cos t, and y = sin t, express dw as a function of t, both by using…

A: The given function is w=8x2+3y2, x=cost and y=sint. We have to express dwdt as a function of t.…

Q: 1. Consider the following function: y = f(x) = In (2r² + 6x + 5), for x > 0 (a) Calculate f'(0),…

A: Using Derivatives & equation of tangent line.

Q: 1 Find 는 dx by using chain rule, if f = u + u = T x , at x = = 4 cos?u

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Q: For ey – In x=y2, find the value of so that & (y' – y') = 1 at y =0- O e e

A: we have to find

Q: Let f(x, y) = x² + y² and r(t) = (cos 1, sin t). (a) Find f(r(1)) without making any calculations.…

A: a) Equation of the circle with the centre at the origin that is (0,0) is x2+y2=a2 then every point…

Q: The equation implicitly defines z as a function of t. Find dz dt 11 dt cos (3 z) = -8

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Q: The tangent line to the curve y=f(x) is horizontal at where X = Xo f f(xx) = 00 A O f(xo) = 00 .8 O…

A: The tangent line to the curve y=f(x) is horizontal at where x=x0 if

Q: Find the G.S.of the DE. (ytu dy=D0

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Q: . Solve the following problems: (a) Utt = 0, 0 0, u (x, 0) = x + sin x, Ut (x, 0) = 0, 0 0.

A: Solution

Q: -8. AB is tangent to to OC at point B. E 6. MZCDA - 8. MZDBA = 32

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Q: 13. Find the derivative of the function T(z) = dz +b cz +d numbers such that ad – bc + 0. When is…

A: Hello. Since your question has multiple parts, we will solve first question that means question (13)…

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

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Q: Solve the following initial value problem for y as a function of x. dy X- 3Dx? -9, х23, у(3)%3D0

A: By using integration formulas

Q: Eliminate the parameter t from the following. S¤(t) = sin t – 4 ly(t) = cos t – 2

A: Separate sin and cos one side then square and add

Q: Consider the function g(x) = 5 S cos t dt – x?. Then g' (x) is

A: Given gx=12∫x4x2costdt  -x2

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: 36 – t2 dt. f(x) 4+ cos? (t)

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Q: 3 If the length of the curve y = 4 xž from the point (0, 0) to the point (xo, f(xo)) is L = ((20737)…

A: Given,          The length of the curve y=4x32 from the point 0,0 to the point x0,fx0           is…

Q: 6. If x= sect and y=tant, evaluate at t =- of the following: dy (a) dx d'y (b) dx?

A: x = sect y = tant

Q: бх? + 4y, : Suppose w = Compute dwldt in two different ways: x = 5 cos(t) +7 sin(t), and y = 5…

A: NOTE-By bartleby rules, only first three question has been answered. As per given by the question,…

Q: 18. The equation of the tangent line to 2² sin T # 0 f(x) = 0 x = 0 at r = 0 is 1 (a) y = -x (b) y =…

A: Note:Since you have asked  multiple questions ,we will solve first question for you.To get remaining…

Q: Q2: find dw/dt at given value point for the following function x= cos°(1), y = sin²(1).= =-. 1 at t…

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Q: 6. Let r = t sin t, y = t cos t, 0<t<1. dy (a) Find dr

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Q: ds Find the function s(t) satisfying = 6 +5 cos t and s(0) = 5. dt

A: It is integration using initial conditions.