Let Y= x² +3 2 d. Find the average rate of Change of Y'o 79 over the following with respect to x intervais. 2. [9,10] 19,957 19,9.1] b. Find the linst antaneous)rate of Change Of Y at

Q: Find the differential dx for the function: y=V4+5x at x 0 and dx 0.04. 0 5 O 0.08 O 0.05 O 0.8

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Q: find a general sulution to the differential eguatiun using variation of A parametert b)yィyニ tantee…

A: Method of Variation of Parameters: This method is quite general and applies to equations of the form…

Q: Use the total differential dz to approximate the change in z= 6-x² – y² as (x, y)moves from the…

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Q: Find the differential of the function f(x,y)=x(e^-y) at (2,0). df=?

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Q: Let y = f(x), where f(x) = Vx + 4. Find the differential of the function. dy =

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

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the integrating factor of the following linear differential equatio rt P. 100 dP dt Select one:…

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Q: a) Determine the average value of the function f(t)=t² – 5t + 6 cos at on the given interval –1,

A: As per guidelines, we will solve only first question. Kindly repost other question separately.

Q: In a mass-spring-dashpot system , the mass’s position at time t isy = 4e-t(sin t - cos t), t ≥…

A: Given: y=4e-tsint-cost, t≥0 The average value of y over the interval 0≤t≤2π

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A: In partial derivatives, the total derivative approximates the function with respect to all of its…

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Q: Q1J Use the Chain rule to find the derivative of w=xy + In z with re spect to v if x v/u, y u+v, z…

A: The chain rule is used to calculate the derivatives of the function. The chain rule for a function…

Q: For the function y=JHx +1 + Find: a) The equation of the tang ent liné at X = 2 b) The equation of…

A: Given,            y=4x+1+2xTo find : a The equation of the tangent line at x=2.                b The…

Q: Let y = tan(4x + 4). Find the differential dy when z 1 and da 0.4 1.631 Find the differential dy…

A: First, let us evaluate the derivative of the given function using the chain rule:…

Q: Find the total differential of the function. 4y f(x, y) 5x - y df =|

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Q: Given z = x²(1 + y}' . (a) Use total differential to approximate (2.03)*(1+8.9) –2²(1+9)'. (b)…

A: Given: z=fx,y=x21+y3 Formula of total differential for z=f(x, y) is given by…

Q: Find the total differential of the function. 5x + у f(x, у, 2) y + 3z df =

A: Total differentiation

Q: Let y = f(x), where %3D 7 f(x) = x + Find the differential of the function. dy =

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Q: Write the differential dw for the function w = ƒ(x, y, z).

A: Consider the given function w=fx,y,z

Q: Find the antiderivative of the given derivative. ds = 5t(212 – 1)3 dt

A: Solution:-  given that  dsdt=5t(2t2-1)3 now  using identity (a-b)3=a3-b3-3ab(a-b)

Q: Find the total differential of the function f(r, y) = (3 y²+6 2):

A: Given,           The function is fx,y=3y2+6x13 .

Q: Find the rate of change of w with respect to / at t = 1 by using the chain rule. You can check your…

A: Given w=x7y3z3     ;    x=t6    , y=t+2    ,   z=3t4

Q: Let y 52?. Find the change in y, Ay when r = 5 and Ar 0.1 Find the differential dy when x 5 and dx =…

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Q: Let y= tanx .(a) Find the differential dy .(b) Evaluate  dy and ∆y if x= and π /4 and dx =-0.1.

A: Given function is (a) Differentiating with respect to x, we get

Q: (a) Compute the average temperature of a wire in the shape of a helix c(t) = (cos(t), to, sin(t)), t…

A: To find- Compute the average temperature of the wire in the shape of a helix ct = cost, t10, sint, t…

Q: Let y = f(x), where f(x) = X - 6 Find the differential of the function. dy =

A: Diffrential is just put function of y and x separate and then just find f'(x). Now put the value of…

Q: Q5. If W = x² y + 2xyz , x = t², y = t + 1, z = 2t at t = 1. Find the total differential

A: Let's find.

Q: Find the derivative of the following integrals: (a) (**at) (b) (LA dt) Vt +1

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Q: Find the average velocity of the function over the given interval. 2) h(t) = sin (3t), |0, D) A) B)

A: The given function is h(t)=sin (3t), 0,π6 We have to find the average velocity of the given function…

Q: Let y = tan x. (a) Find the differential dy. (b) Evaluate dy and Δy if x = π/3 and dx = -0.2…

A: Let,  y=fanxa To find differential dy, differentiate y       with respect to x,        dy=sec2x dx

Q: Let f(t) = 4 sin(at) measure the height of waves in Horsetooth Reservoir with respect to time in…

A: The height function of the waves with time is ft=4sinπt

Q: H.W: Use the chain rule to find the derivative of w= x² + y² with respect to t dw dt with x = cost +…

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Q: Find the approximate value for f(z, y) = sin(x5zy+ ln(y)) at (0.03, 1.04). Taken = 3. 00,24 O 0,14 0…

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Q: Q2: Suppose the electric potential at (x, y) is given by f(x, y) = 0.5 Ln(x² + y²) estimate the…

A: In this question, we have to find the error in f(x,y) and percent relative error for the given value…

Q: H.W: Use the chain rule to find the derivative of w= x + y with %3D dw respect to t dt with x =…

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Q: Find the rate of change of w with respect to / ati = 1 by using the chain rule. You can check your…

A: Here, w is the function of x,y, and z and x,y, and z are functions of t where…

Q: Find the total differential dw. 4. w = e*" – sin(yz) -

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Q: ) L(3.98) where L(x) is the linearization of y = √√x +3 at x = 1 (tangent line approximation)

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Q: Find the differential of the function. 7 + uvw Da + | Dov•([ Daw dT =

A: Given function is By using quotient rule of differentiation

Q: Find the total differential z = e−x tan y

A: we have to find the total differential of z = e−x tan y           dz=∂f∂xdx+∂f∂ydy        (1) where…

Q: Let y = f(x), where   f(x) = 4x2 + 6.   Find the differential of the function.   dy =?

A: Given: y=fx=4x2+6 now differentiating given function with respect to x

Q: Find the differential of the function f (x, y) = xe at (-3,0). df =

A: Explanation of the answer is as follows

Q: Let y tan(3x + 6). Find the differential dy vwhen a 2 and da 0.4 Find the differential dy when z 2…

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Q: H.W: Use the chain rule to find the derivative of w = x² + y² with dw respect to t dt with x = cos1…

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Q: Let y = 4/T. Find the change in y, Ay when x = 1 and Ax = 0.3 Preview Find the differential dy when…

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Q: 5t+3xy 5. For z = and x = t2 + 1, y = \t² + 1 and w = e* + 1, calculate the total derivative, 2w²y…

A: Given,            z=5t2+3xy2w2y and x=t2+1          y=t2+1 and w=et+1

Q: Find the total differential. z = 6x *y5 iz

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Q: Find the antiderivative of the given derivative. ds = 14t(5t2 – 1)3 dt S=

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Q: Can i get help step by step please

A: Given expression.

Q: Let f (x,y) = 3x e with x(t) = 9 e and y(t) = t. Find the derivative of w f(x,y) with respect to t…

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