Let f:[-n, 7] –→ R, where f(x) = 2 sin (2x) – 1. TC Calculate the average rate of change of f between x =-– and x = 6. a.

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A: Given function is, fx,y=sin3x+2πy+exy-π. To find the rate of change of f at A(π,1) along the…

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A: Given: The function y=tan-1ln3x, To determine: The derivative of y with respect to x,

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Q: Let y = V7- x. Find the differential dy when a = 4 and dx 0.3 -0.0866 %3D %3D Find the differential…

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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: Let y = f(x), where f(x) = 5x² + 5. Find the differential of the function. dy = X

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Q: Let y = tan find the differential dy of the function.

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Q: Evaluate the integration of the function. f(x) = 1+ e-x sinan over the fixed interval [a,b] = [0.1]…

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Q: Let y = tan(5z + 6). Find the differential dy when a = 4 and dæ 0.1 %3D Find the differential dy…

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Q: Let y = f(x), where f(x) = 7x³ + 3x. Find the differential of the function. dy = X

A: The differential of y is the derivative of the function times the differential of x,

Q: Find the differential of the function y=1/√u2+v2, where u and v are differentiable functions of the…

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

A: Given fx=sin9x Differentiate fx=sin9x with respect to x, we get f'x=ddxsin9x=9cos9x Hence,…

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

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Q: Use the differential dz to approximate the change in z = √4 − x2 − y2 as (x, y) moves from the point…

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Q: Find the derivatives. a. by evaluating the integral and differentiating the result. b. by…

A: Given that: ddx∫0x3 e-t dt To find: a) By evaluating the integral and differentiating the result. b)…

Q: Let y be a function of x . If y“ = tan(x² +y² ) + e®, find dy by implicit differentiation. dx

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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: . f(x, y) = y*e*Y at (0.2, 1.96)

A: Use differential formula to find approximate value.

Q: Find the total differential of the following: 1. f(x, y,z) =-tan'(x + y +z)+ In(xyz)

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Q: let f(x,y)= z-sin(xy),x= t, y= lnt, z=e^t-1. find derivative of f directly and by using chain rule…

A: Plug the given expressions of x,y, and z. Then differentiate directly. And plug t=1

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: Write the differential dw in terms of the differentials of the independent variables. w f(x,y,z)-…

A: To calculate the total differential dw for the given function of three independent variables

Q: (a) Integrate the following function; i) SG) dx 1+9x² ii) S dx (b) Differentiate y = cosh-1(x² + 1)…

A: 5(a) (i) Given integral is ∫91+9x2dx ∫91+9x2dx=9∫1919+x2dx=∫119+x2dx=∫1132+x2dx Hence,…

Q: Use the differential dz to approximate the change in the function z (shown in the image) as (x, y)…

A: Given that:   The given function z = f (x, y) moves from the point (1, 1) to the point (1.03, 0.95),…

Q: Find the derivatives. a. by evaluating the integral and differentiating the result. b. by…

A: To find derivativeddt∫0tx4+31-x2dx (a) By evaluating the integral and then differentiating the…

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 f(x, y) = 2x − 3 cos(xy) + 4y. Find the rate of change of f with respect to t along the path…

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Q: 3. ) Compute for the increment of the function f(x,y) = *+3y . Also, find the total differential of…

A: w = f (x, y) and let ∆x and ∆y be increments of x and y respectively. The increment ∆w of w = f (x,…

Q: Find the linear approximation of the function at the given point: f(x, y) = 2 sin x – 3 cos y at (0,…

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Q: Where is the function f(x, y) = e' arctan (VI+In(x+y)

A: In this question, the concept of continuity is applied. Given function is fx,y=etan-11+lnx+y

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

Q: Suppose that x and y are both differentiable functions of t and are related by the given equation.…

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Q: Let y = tan(3r + 4). Find the differential dy when z = 2 and dr 0.1 %3D Find the differential dy…

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Q: H.W: Use the chain rule to find the derivative === with x = cos² t, y = sin² t, z = - at t = 3 dw xy…

A: Solution :

Q: Find the rate of change of f with respect to t along the curve. f (x.y,z) =y² - sin(x +z),7(1) =…

A: According to the problem, we have

Q: b) Find the value of the derivative of f(x, y, z) = xy + yz + xz with respect to t on the curve x =…

A: There are two methods to do this: One is direct method which we used and other is by chain rule.

Q: Let y = f(x), where 3x? f(x) : Зx + 4 ,2 x + 4 Find the differential of the function. dy =

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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 derivative of the function at Po in the direction of A. g(x, y, z) = 3e* cos yz, Po(0, 0,…

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Q: Find the differential of the function. Z = e-8x cos(5xt) dz z = dx + dt %3D

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Q: Find the total differential of the following: 1. f(x, y) = sin x+ ye 2. f(x, y, 2) = – tan"(x+ y+ z)…

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Q: implicitly dx

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Q: Let W=x*yz.compute the differential dw.

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Q: 4. Find the total differential of z = In(x + y), x= w, y = w². By how much will z change if w…

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