3. Given a function z = x2 + xy°, and x = cost, y = sin t, evaluate when t = T. dt

Q: If z = xe" and x = t2, y = Vt then the value of dz at t = 1 is equal to . dt Select one: True False

A: Solve the following

Q: If x= sint and y = cost then 2 dx dy dt dt O 2 O -1 O 1 O O O None of these

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Q: Find the total differential dw. 1 5. w = x tan¬' y – 2ªyz -

A: Solved below

Q: Use Euler's method with h = 0.25 to compute approximate value of y(1) for the IVP: (a) dy 1 = y sin…

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Q: Suppose y = (x + 1)5, and both a and y are functions of t. If. dy :1, find dt dx when x = = 1. |3D…

A: Given data:   The given function is y=(x+1)5. The first value given is dy/dt=1. The given value of x…

Q: Given a6x CosT+Sy - .3x. -Siny+ 10x-e -*, defermine (1) T'=S(T) ax T'-

A: Given:T"=6x2y3-cosx+5y2-siny+10x2-e-3xTo determine:i  T'=∫T"dxii  T'=∫T"dy

Q: dz evaluated at dt If z=tan In with x=sec t and y=eª. Then the value of t= 0 is equal to ...…

A: Chain Rule Let us consider the function z=f(x,y) where, x=g(t) and y=h(t) Differentiate the function…

Q: dt z = cos(x + 4y), x = 5 t ³, y = 8/t

A: We need to find out the value of dzdt

Q: Find dw/ dt at the given value for the following functions dw dt 1) w= x + y°, x= cos(t), y= sin(t),…

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Q: The velocity of a particle moving back and forth on a line isy = ds/dt = 6 sin 2t m/sec for all t.…

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Q: Given z = z?xy – tan(xy) where x = sin (5t + 2) and y = t3 + 4t. By chain rule, || dz find dt

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Q: Find dw/ dt at the given value for the following functions Z 2 X Y x= cos² (t).y = sin² (t).= = =,…

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Q: a - Find h (Stet sinh t sint dt)

A: The objective is to find ∫te-3tsintsinhtdt It is known that, sint=et-e-t2isinht=eit-e-it2…

Q: 2.f(t) = cosh wt sin wt

A:

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 z=x²y+3xy, x=sin(2t), y=cos(t), find dz/dt when t=0

A: ddxcosx=-sinx

Q: (c) Prove that L{Cost Si(t)- Sint Ci(t)} Logs s +1 %D

A: The complete solution is in given below

Q: The velocity of a particle moving back and forth on a line is v = ds/dt = 6 sin(2t) m/sec for all t.…

A: Given:

Q: dw by using Chain Rule. (Your answer should not include z ond y. dt = z+v? z = cost + sin t and y=…

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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: dw at the given value of t: dt Evaluate w =x2+y x = cost +sint y = cost -sint %3D 2.

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Q: How can I evaluate ∭x2 dV, where E lies between the spheres ρ = 1 and ρ = 3 and above the cone Φ =…

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Q: (a) f(x) + cosh(47) (b) f(z) = VI In(|tan(9r)|) tan n(x) psin(z) 12 (c) y = dt

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Q: The linear approximation at z = 0 to sin(4z) is A+ Bz where A is: and where B is:

A: Linear approximation is found by L(x)=f(x)+f'(x)(x-a) Differentiate L(x) with respect to x.…

Q: Find dw/dt at t=0 for the function w=sin(x),cos(y),ln(z). Where x=-7t^2+9t+pi/2, y=t,z=e^-6t

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Q: show that the Punctionc Sinh t V3 and ye T5 Sinh t+ CoshE 13 taken together satisfy thediff erential…

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Q: Let y = tan(3r + 4). Find the differential dy when T = 4 and da 0.4 Find the differential dy when x…

A: Given: Differentiate the above expression of 'y' with respect to 'x'.

Q: Find the length of the curve y = ln sin x from t = −2 to t = 0.

A: f(x)=y=ln(sinx) Arc length =∫ab1+(f'(x))2dx f'(x)=dln(sinx)dx=1sinxdsinxdx=cosxsinx=cotx a=-2 b=0

Q: Find dw/ dt at the given value for the following functio 1) w=x² + y°, x = cos(1), y = sin(t), at †…

A: The given functions are w=x2+y2, x= cost  and  y=sint and t=π. Evaluate w in terms of t as follows.…

Q: Evaluate dW at t = dt for the function W = xy x = sin t, y = cos t, z = t². 4 49л2 972 9x2 4 49л

A: Given: W=xyz,x=sin⁡t,y=cos⁡t,z=t2 Substitute the value of x, y and z in w , we get W=sintcostt2…

Q: Find the general antiderivative of the given function. f(x)= sin (7y)+ cos (3y)

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Q: Q1-If x= cot-1 VE, y = find dy d2y dx' dx² at t = 2. t+1

A:

Q: Find dw/ dt at the given value for the following functions 1) w=x² + y²₁ x = cos(t), y = sin(t), at…

A: Sol

Q: a(22) V17 – cos(2nt)" (2 – 4) sin() 1. Given f(x) dt, find the equation of the line tangent to the…

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Q: dw/ dt باستخدام قاعدة السلسلة ، فإن W=x? + y? X=cos t y=sin t = 0 = اللانهاية لا أحد من الآخر = 2…

A: Use differentiation

Q: If r = (cost)i + (sin t)j + 2tk, find r × dr/dt.

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Q: If y = 1+ sin t ,x = cost at t = Findy by using Chain Rule, then choose the correct answer: dt

A: Given that: y=1+sintx=cost

Q: at and ду ду Suppose that 3x - 4y = t and y =t sin 0. Find dt

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Q: Find the value(s) of at y= 1 given that x2y+y2 = 5. dx

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Q: 10 ( °j + t°k)dt ti + t

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Q: 2.f (t) = cosh wt sin wt

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Q: Given x = 2 cost +33 and y=8 sin t |3D da dt dy dt dy dx

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Q: Solve the following problem dw dw + x dt 1, -00 0, %3D dx with w(x, 0) = f(x).

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Q: The velocity of a particle moving back and forth on a line is y = ds/dt = 6 sin 2t m/sec for all t.…

A: given the velocity of a particle moving back and forth on a line is y = ds/dt = 6 sin 2t m/sec for…

Q: (dr Ifr=a cos ti +a sin tį+ at tan 0 k, find dt dr at t = 0. dr?

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Q: 1. Given xy = sin x , show that d'y 2 dy +=+y = 0. dxx dx

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Q: If x = 3 sin* t and y = 2 cos" t , then find dy at t = dx 4

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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: dw b) If w = (x + tanx). (Vx – 1), and x = tan (cost) find dt

A: