Find the linearization of the function f(x, y) 155 – 2x2 – 5y² at the point (5, 4). L(x, y) = Use the linear approximation to estimate the value of f(4.9, 4.1) = %3D

Q: 324y/" – 180y' + 25y = 0, %3D y(0) = 8, y'(0) = 5. y =

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Q: Estimate the IROC for the function f(t) =Ax) = x² – 20x

A: Given: fx=x2-20x To find the instant rate of change, Differentiate the given function with respect…

Q: Find y as a function of x if

A: The given differential equation y'''-4y''-y'+4y=0D3-4D2-D+4=0D+1D-1D-4=0D=-1, 1, 4

Q: 1. y = Vz + 3z – 1

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Q: Consider the function: f (x,y) = 2x² - 4x - xy² + 2y² - 3. Explain how you would find the first &…

A: We have given function f(x,y) = 2x2-4x-xy2+2y2-3  We have to find the first & second-order…

Q: Find the direction in which the function increase and decrease most rapidly at point Po. Then find…

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Q: Differentiate the function. = In({ (4t+ 1)³ (4t-1)5 F'(t) = F(t) = In

A: The derivative of the function in the division form is given by the quotient rule which is given by-…

Q: Find the average rate of change of f(x)=−x2+9x on the interval [1,6].

A: Given: The given function is, f(x) = -x2 + 9x  on [1, 6]   To determine: The average rate of change…

Q: Differentiate the function f(t) = yt (a + bt).

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Q: Differentiate the function f(t) = t (11t+ 2). Answer f'(t) =

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Q: Determine the directional derivative of f at the specified point and direction. f(x) = x³ + y³ – 3x?…

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Q: Find y as a function of t if 25y"- 70y' + 53y = 0, and y(5) = 8, y'(5) = 1. %3D y = %3D

A: Given: 25y''-70y'+53y=0  with the IVP y(5)=8 ,    and   y'(5)=1By…

Q: Use Linear Approximation to estimate Af f (2.05)-f(2) for f(x) = %3D x+I (Use decimal notation. Give…

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Q: Let f(x) = V1+x. Estimate the change in f from x = 7 to x = 7.5 using linear approximation. %3D

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Q: 49y" — 42y + 5y = 0, and - y(4) = 4, y'(4) = 1. y =

A: 49y''-42y'+5y=0, y(4)=4, y'(4)=1 Auxiliary equation 49m2-42m+5=0

Q: (m) y = f (n) y = f x +3 V1-x² dx x² + 10x + 30 2 -dx.

A: Solve the following

Q: (x² – y²)² – 4ay³ = yCosx + xCosy = 1

A: We have to find the derivative of the above functions .

Q: f(a + h) – f(a) 3. Find a and h such that is equal to the slope of the secant line between (3, f(3))…

A: Slope of the secant line is,

Q: Find the linearization of the function f (x) = a° at a = 1.

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