Suppose r(t) = cos(nt) i + sin(at) j + 5tk represents the position of a particle on a helix, where z is the height of the particle.

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Q: Consider the following IVP: y" +y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

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Q: Let y tan(5x + 8). Find the differential dy when I = 5 and dr 0.1 Find the differential dy when I 5…

A: y=tan(5x+8)Differentiate on both sidesdy=sec2(5x+8)×5×dxSubstitute x=5  , dx=0.1…

Q: 5.32. z = sin(x² + y?)

A: To find the differentials of third order.

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Q: If k 0 then the trigonometric integral [ 3 sin³ (kx) dx is equal to ¹(3 cos(kr) cos³ (kr)] + C

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Q: Let y tan(4x + 6). Find the differential dy when x = 5 and dx = 0.2 Find the differential dy when x…

A: Given : y = tan(4x + 6)   To find the differential dy when x = 5 and dx = 0.2 Also to find the…

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Q: azz = e2x-y + cos(-3x + 2y) + 3x, дхду Given that az where əx 5x2 – sin (3x) when y = 0, and Z =…

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Q: A particle moves along the x-axis with velocity given by v(t) = 6T sin (2nt) for time t > 0. If the…

A: Given: vt=6πsin2πt at t = 1, x = -4

Q: Let y = tan(3r + 5). Find the differential dy when x = 3 and da = 0.1 Find the differential dy when…

A: Here we need to use chain rule of differentiation to find dy. According to chain rule,…

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Q: S2ta J 2tan x In (cos x) dx=

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Q: Compute for the arcsinx dx . Which of the following is not an antiderivative of the function f(0) =…

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Q: Let y = tan(3x + 6). Find the differential dy when x = 2 and dæ 0.2 Find the differential dy when x…

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Q: Q:: If In /x2 + y? =sec(), use implicit differential to proof the following: - dy -x-(x2+y²). sec.…

A: Please see the explanation below..

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A: Given acceleration, a(t)=cost,       t>0 And v(0)=0, x(0)=3

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A: y=tan4x+3

Q: Let y = tan(4x + 7). Find the differential dy when x = 2 and dx = 0.3 Find the differential dy when…

A: Since you are asking multiple questions. We are answering only the first question as per our…

Q: Let y = tan(3x + 7). Find the differential dy when a = 4 and dæ = 0.3 Find the differential dy when…

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Q: 2 2メ Q1 find dy for y = Cos ( In x + e

A: we have to derivative with respect to x

Q: Let y = tan(2x +5). Find the differential dy when x 3 and dr = 0.1 Find the differential dy when z =…

A: Given that y=tan(2x+5) find the differential dy when x=3 and dx=0.1 find the differential dy when…

Q: dx y of y = cos 1 (In (xy)) Find %3D CoS dy

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Q: D. 1. If (x + y)² = x² + y² 2. If y = sin³ () cos³ () dy - dx X prove that y' = sin² (x) cos(x) 8…

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Q: Show that where n is a positive integer.

A: To show

Q: 2. Show that the LT of sin(wt) is L sin(wt)] (s) where w is a positive constant.

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Q: Let y = tan(5x + 6). Find the differential dy when x = 5 and dx = 0.2 Find the differential dy when…

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Q: Let y tan(4x + 8). Find the differential dy when x 5 and dx = 0.2 Find the differential dy when x =…

A: Topic = Derivative As per guidelines , At a time only one question can be answered.   use formulalet…

Q: Let y = tan(4r + 8). Find the differential dy when a = 4 and da = 0.3 Find the differential dy when…

A: Differential equation: - A differential equation is an equation that contains the derivative of an…

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A: The velocity of the function is given as:

Q: The linear approximation at x = 0 to sin(6x) is A + Bx where A is: Preview and where B is: Preview

A: First of all, consider the formula to find the linear approximation at any point a for function any…

Q: Q4. Given that: z = y sin(2x) + (1+x²)e* + cos x tan-1(y* + 1) In(y6 + 137)

A: Given that, z=y sin2x+1+x2ex+cosx tan-1y4+1 lny6+137 ∂z/∂x is the partial derivative of z with…

Q: HW 0If y=tanx show that- yl" =-2 Siny coży

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Q: A particle moves along the x-axis with velocity given by v(t) = 3T sin (t) for time 10 at time t =…

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Q: Let y = tan(4æ + 5). Find the differential dy when a = 5 and da 0.2 %3D %3D

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. @ y(x)…

A: We find the general solution of given DE  y"+y'=-cos(x)........(1)

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Q: Let y = tan(3x + 8). Find the differential dy when x = 3 and dæ = 0.1 Find the differential dy when…

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Q: dy.xandy in =cos = COS e

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Q: A particle moves such that its velocity at time t is given by: v = 3t2i + 2 cos(4t)j + t2k If its…

A: given velocity of the particle at time 't' v=3t2i+2cos4tj+t2k initial position x(0)=2i

Q: Let y = tan(3x + 5). Find the differential dy when a = 4 and dæ = 0.1 Find the differential dy when…

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Q: Determine the general solution of (cos(x)cos(y)-cot(x))dx=(sin(x)sin(y))dy

A: Given: cos(x)cos(y)-cot(x)dx=sin(x)sin(y)dy

Q: Let y tan(3x + 2). Find the differential dy when x = 4 and dæ 0.2 Find the differential dy when a =…

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