Given R(t) = 2 sin(t) i + 2 cos (t) j + 2t k   f What is the direction at t= pie/2

Q: Find impicitly, tf e*(eУ — 1) + sin(2x + 5у) %D In(V7) - - сot(2x) y+2

A: Given function is Differentiating with respect to x by using product rule ,we get

Q: Find the length of the curve. cos(4t) i + sin(4t)j + 4 In(cos(t)) k, 0 <t< n/4

A: We have to find the length of curve.

Q: Find the general solution of the following first-order ODE xy' = y + 2x3 sin?

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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: Find the coordinates at t = 0, π/4 , π of a particle moving along the path c(t) = (cos 2t,sin2 t).

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Q: (a) If y = tan x, prove that y = 2(y2 + 1)(3y2 + 1). (b) Find y' for y cos(sin?x). %3D %3D dy (c) If…

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 4 cos x – sin xy; y = 7t || Enter the…

A: We have to find

Q: Q1: If Z= x^3+y^4+(x sin y)+ (y cos x), Find Zxx? Zyy? *

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Q: Given that y = sin (t) and x cos²(4t*), hence find dx dy

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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: 3. If G = (2x²y – x*)î + (e*y + y sin x)j+ (x² cos y)k, find: %3D дхду

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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: Solve the following problems by applying chain rule. dw (a) If w=x -2y² +z', and x= sint , y=e', z=…

A: We have to applying chain rule and solve given problem

Q: and as Use the chain rule to find sin(6) r = st, 0 = s + t3 dz as

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Q: d²y Given that y = -4x cos 2x +4 sin 2x, find dx² at x = 2

A: Given: y=-4xcos2x+4xsin2x

Q: Consider y@) + y" = 1+ cos( - t) Then a suit- able form of the particular solution can be written as…

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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: Given z(x, y) =In(2xy) where x(u,v)= e" cos(4v) and y(u,v)=e" sin(4v). Find ди 1 cos (4r)+-sin(4v)…

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

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Q: Find a positive value of k for which y=cos(kt) satisfies y''+25y=0.

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Q: Suppose A(t) = [ e^t 0 0 0 cos t sin t 0 −sin t cos t]…

A: Given: At=et000cos tsin t0-sin tcos t To Find: To show that At-1 exists and then to find it.

Q: If x = 3 sin t and y =2 cos* t , then find dy at t = dx 4 O a. -0.67 O b. 0.76 O C. 0.56 O d. -0.86

A: Given x=3sin4t   ,y=2cos4t

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

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Q: 3. f(t) = 2e3t sin 2t 3est cos 2t %3D -

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Q: If y = (2x² – 3x+4)(e¯* – cos 4.x), then find dy at x = 0 dx

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Q: Suppose that w = x² + y? + z², x = cos 0, y = sin 0, z = tan 6. Use the chain rule to find dw when 0…

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos a – sin xy; x = - y = 4t t'…

A: This question is based on Derivative of Function.

Q: Given f(x,y,z) = cos(4xy) + sin(2z). Find fy(1,2,0). Leave your answer correct to two decimal…

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Q: If f(z, y) = e sin 8y, then fzy is given by: O 16 e sin 8y 16 e sin 8y O 16 e cos 8y 27 16 e cos 8y

A: We can solve it by taking partial derivative of both side two times as below

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: Q6A)If y = sin-¹ prove Zyy + 2 = 0

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Q: The value of 'b' for which u(x, y) = ebx cos 5y is harmonic

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Q: ди ди then x +y = u. 31. If u = Jy² - x2 sin-

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Q: Find the solution of the equation 22 J²z Əz + =e cos y dx² Əy² which tends to zero as x→∞ and has…

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Q: Find r(t) for r'(t) = 2/ti + 3 cos(2nt)j – e-'k and the initial condition r(0) =i+2j

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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: Given f(x,y,z) = cos(5xy) + sin(4z). Find fx(6,6,0). Leave your answer correct to two decimal…

A: Given f(x,y,z) = cos(5xy) + sin(42). Find fx(6,6,0)

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

A: Solution

Q: dz Use an appropriate form of the chain rule to find dt 1 8 cos x sin ry; y = 9t t' Enter the answer…

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Q: If x = 2 sin* t and y = 3 cos* t, then find dy at t = %3D dx 4 а. 1.5 b. -2.5 с. -1.5 d. 2.5

A: Solution:

Q: Let F(t) = (e' cos t) î+ (e' sin t) ĵ + e' k. %3| (a) Find symmetric equations of the line tangent…

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Q: If f(x) = (e'7 cos(x))' 18e +12 sin(r) f'(0) then %3D f(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: Given G(x, y) = y* sin(2x)+x² ( x0 º – cos(y²))' find Gyyyxxxy „10 ууххху

A: Consider A(x,y)=y4sin2x and B(x,y)=x2y10-cosy27 then G(x,y)=A(x,y)+B(x,y).Therefore…

Q: Find the particular solutions satisfying the given conditions: dy a) y = 2 when x = 0. dx = 1 + cos…

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

Q: If w = Vr + y² + zª where r= sin(0), y = cos(@) and z = Use the Chain Rule to find tan(@). dw when…

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

A: This question can be solved using the concept of partial derivatives.

Q: The linear approximation at and where B is: = = 0 to sin(9x) is A + Bx where A is:

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos x :- sin ry; y = 9t Enter the…

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