d [sin(t) dt = sin(Vk), Where k is cons tant Select one: O True O False

Q: If u = x² cosy+ ye", where x = s+2t and y = st, prove that ди ди 2- (s – 21) (x siny- xye – e"). -…

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Q: | cos zdr + sen ydy + x?dz

A: The solution are next step

Q: Let V = eP cos(qr), with p = x In(xyz), q = z cos(Ty) and r = 2 tan-(y). By using the chain rule,…

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Q: If f(#) = | cos(t) dt, then f'(2) = s(t²) dt, then f'(x)%3= COS Select one: a. 3e cos(2) CoS b. e…

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Q: Compute r"(t) and r(t) for the following function. r(t) = (cos 2t, sin 3t, cos 6t)

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Q: Let x (t) =y(t) +sin(t), x2(t)=y (t) then x2(t)= x,(t)- cos(t) Select one: O True False

A: given x1(t)=y(t)+sin(t) , x2(t)=y'(t)

Q: 4. Evaluate + tyt - 1j+t sin at k) dt

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Q: If u(t) = (sin(2t), cos(2t), t) and v(t) = (t, cos(2t), sin(2t)), use Formula 5 of this theorem to…

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Q: Compute r' (t) and r'"'(t) for the following function. r(t) = (cos 4t, sin 3t, cos 2t) %3D

A: If, r(t) =<f(t),g(t),h(t)> , where f(t), g(t) and h(t) are differentiable functions,   then…

Q: If u(t) = (sin(4t), cos(2t), t) and v(t) = (t, cos(2t), sin(4t)), use Formula 4 of this theorem to…

A: Find u(t) . v(t) first then differentiate with respect to “t”.

Q: y=6 In(cos(e7")). dy AeBt sinC (e7 dt Then %3D cosº (e7) where A = %3D %3D D = BCD

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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: If y=sin( x2 + 1), then compute y O A. xsinx² +1) y = Vx2 +1 O B. None of the other choises cos(/x²…

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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: dy Find xp y%3D COS dt

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Q: Let F = (e^5(y), sin^2(x), cos^4(x)). Calculate curl(F).

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Q: Find dy/dt, x=4 sin t; y=12 cos t* O 24 cos t O -24 sin t O 12cos t O -12sin t

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Q: Suppose that w = a7 · exp(2y) · cos(4z) with z- in (+ 5), x = sin (t+ y = In (t +2), z = t.

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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: Find the linear approximation to g(z) = cos(z + 1) at z = 0. Use the linear approximation to…

A: The formula to find the linear approximation Lz of a function fz at the point z=z0 Lz=fz0+f'z0z-z0

Q: Verify that the indicătéd function is an exp for each solution. y" - 6y' + 25y = 0; y = e3x cos 4x…

A: Recall: (uv)'=u'v+uv' where u and v are the function of x

Q: Q5. Evaluate the triple integral cos(y²) dz dx dy.

A: The given triple integral is;  Cos(y2), z from 1 to 3, x from 0 to y, y from 0 to sqrt(pi/2).

Q: If f(z) = cos(t) dt, then f'(z): COS %3D Select one: a. 3e cos(z) COS b. ez cos(ez) c. 3e cos(e)…

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

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

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Q: Evaluates t cos(2t*) dt

A: here we will put 2t4 = u then solve further

Q: d. sin(t) dt =0. Where k is cons tan t dx %3D Select one: O True O False

A: We will use the formula ddx∫x0x1f(x,t)dt = ∂∂xf(x,t) + f(x,x1)x1' - f(x,x0)x0'

Q: (a) Evaluate where c is z = 1 %3D c cos(Tz)

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Q: Let z = x?y + 3xy+ where x = sin 2t and y dz find = cos t. Use the chain rule to when t = 0. dt

A: See solution below. Using definition of chain rule.

Q: 3. Evaluate the following: cos1(t)dt C. dx b. J Jezx-1 In(x)dx V1-t2 a.

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Q: (b) If u =x cosy+ ye», where x=s+2 and y= st, prove that 2- ds du - (s - 21) (* siny-xye -e").

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Q: Use the convolution theorem to show that cos T sin (t – T) dr 1 sin t. %3D 2

A: Convolution theorem use integration of product of 2 functions and transforms them to pointwise…

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: Let T = x²y - xys + 6x, where x = r cos 0 and y = r sin 6. Use the chain rule to find dT/00.

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Q: If u =x² cos y +ye», where x =s+2t and y= st, prove that ди 2- Əs ди 3 (s— 21) (х' siny — хуе" —…

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Q: Let z = x*y + 3xy* where x = sin 2t and y dz find = cos t. Use the chain rule to %3D when t = 0. dt

A: z=x2y+3xy4where x = sin 2t and y = cos t We need to find dzdt when t =0 Let's use the chain rule :…

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

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Q: - Show that u(x,t) e-a't[A sin(2x) + B cos(Ax)] satisfies the PDE uz = a?uxx for arbitrary A, B and…

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

A: Solution

Q: Calculate $ |z|=1 z²e¹/z cos(1/z) dz.

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Q: Compute r" (t) and r"(t) for the following function. r(t) = (cos 3t, sin 6t, cos 2t)

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Q: Use Fundamental Theorem of Calculus to evaluate the following: d a) sin t dt dx

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Q: dw 3) Find ifw = 5 cos(xy) – sin(xy),x = ,y = t,z = t³ - %3D dt

A: Given: w=5cosxy-sinxy, x=1t, y=t, z=t3 For finding dwdt, first we find w in terms of t So, we put…

Q: Find the convolution of f(t)=cos(t)f(t)=cos(t) and g(t)=cos(2t)

A: Given function is f(t)=cos(t) and g(t)=cos(2t)

Q: Calculate the Cauchy principal value. 8 COS X V.P. Leta -dx, (a > 0). (a²-x²)

A: We solve by using residues.

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: Let z=In(x²+y²) where x=ue"sin t and y = ue"cos t. If u=- 2 and 1=0 then is equal to %3D ....

A: Multivariable function: When a function f has more than one independent variable and only one…

Q: If r = sin (ƒ(t)), ƒ(0) = pai/3, and ƒ′(0) = 4, then what is dr/dt at t = 0

A: Given:

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…

Q: 5. Find Sp√x² + y² dr, where ř(t) = t cos t tsint Ost), 0 ≤t≤ 2π.

A: Given r→(t)=tcosttsint,0≤t≤2π. The objective is to find ∫Px2+y2dr.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.