Find the linear approximation of the function f(x) = V1– x at a = 0. L(x) = Use L(x) to approximate the numbers 0.9 and v0.99. (Round your answers to four decimal places.) V0.9 = V0.99 = Illustrate by graphing f and the tangent line.

Q: Find the derivative of the function 1-x2 t2sin(t) dt g'(x) =

A: First I have written the Leibnitz rule for derivative of an integral and using them find the…

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

A:

Q: Find the directional derivative of the following function at P(1, 0) in the direction that produces…

A: Given  fx,y = -3x2+4y3+2xe32y

Q: Use differentials to approximate the change in y = f(x) from x = 4 to x = 4.1 for the function, f(x)…

A: It is given that,

Q: Find the derivative of the function

A: Given  that y = ( ax+ √(x2+y2)) -2 Method used- Chain rule- The chain rule states that the…

Q: Find the derivative with respect to x of the function r4x t² F(x) = e dt.

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Q: Find the derivative of the function. A y = 7tan-(x - V1 + x²) %3D (2* * I^ -

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Q: Q2. Find the slope of the tangent line to the function f(x)= at x 4 by using the 2Vx definition of…

A: Given that,

Q: 2. Given: y = f (x) = (2x-2 + 5x³). What is the slope (gradient) of the first derivative function at…

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Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

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Q: Find the derivative of the irrational function y=m√xn where m≠0

A: we have to find the derivative of the irrational function y=mxn

Q: 2. Find the derivative of the function f(x, y) = 2x² – y² at the point M = (1,1) in the direction…

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Q: Supose z is implicitly defined by the equation qy+ 3x + xyZ + 32=9 in an enmrament of the point…

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Q: Find the derivative. f(x)= | t lInt dt . e

A: Consider the function  f(x)=∫e extlnt dt

Q: (a) Find the derivative of fix. y. 2) = x-xy-z at P1, 1,0) in the direction of v = 2i- 3j + 6k. (b)…

A: The directional derivative of a function f(x,y,z) at the point (x,y,z) in the direction of vector v…

Q: Q2// A) Derivative following functions by using chain rule m 1) y = Vu, 2) y = 4u, -Va+1 Vx+1

A:

Q: Let ƒ(x) = √2x + 1. Compute ƒ'(2),the derivative of ƒ at x = 2, and use the result to find an…

A: Consider the given function, fx=2x+1 differentiate with respect to x, f'x=ddx2x+1=122x+1·2=12x+1…

Q: Q2: - Find the second derivative of the following function at x = 2 15 marks 1) y=+ V 2) y 3 (x +)…

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Q: Find the derivative of a linear function y=ax+b using the definition of derivative.

A: The derivative of a function f' of function f is defined as f'x=limh→0fx+h-fhh

Q: Consider the function f (x, y) = x²y³ – 3xy³. Compute the value of the derivative frvy at the point…

A: Given function is f(x,y) =  x2y3 - 3xy3 we have to find fxyy at the point (2,1).

Q: Find the derivative of the following functions by applying "Delta Method". Show your complete…

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Q: Estimate the indicated derivative by any method. x = 4t + t2; estimate ds/dt | t= -2

A: Given, x=4t+t2 We have to find dxdt at t=-2 We will use following formula to differentiate the…

Q: Q2: A) Find an equation of the line tangent to the function of x2 + (y-x) = 9 at x = 1. dy x-x B)…

A: Equation of tangent line is - y- y1 = m(x-x1)

Q: Find the differential d5y of the function y=lnx2.

A: y = lnx2 = 2lnx

Q: Find the linearization of the function f(x)=ln(2x+3) at x=-1

A:

Q: The derivative of the function y = x² In(x + 1) is:

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Q: 2) Find the derivative of the function. T(r) = ar² + 2e" + n². %3D

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Q: Ax) = Vã Vx = /x хх e

A:

Q: The derivative of the function y = tan(In(vx² – 6x + 1)) is: %3D

A: Formula:ddx(tan x) = sec2xddx(ln x) =1xddx(xn) =n xn-1

Q: Find the derivative of the function f(x) = V (x² – 2)* at x = 1.

A: Given f(x)=(x2-2)23      ⇒f(x)=x2-2213⇒f(x)=x2-223

Q: The only function whose derivative is itself is y = e*. a. True b. False because y = 2ex is another…

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Q: Find the derivative y′(x) of the function that describes the general equation of a second order…

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Q: Consider the function f(z) = V1+z -1 and find its derivative:

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Q: %3D 10. Find the derivative of the function )= V 5T4 using the limiting process.

A: Given,

Q: 3. Find the derivative of f(x, y, z) = z2 + ye" at (In 2, 2, 1/2) in the direction in which the…

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Q: Q4. Find the slope of the tangent line to the function f(x)= e* +3; x+2 at x=4 5x-10

A: Given : fx = ex5x-10

Q: Q2: - Find the second derivative of the following function at x = 2 1) y=+ V

A: ddx1x = -1x2 ddxxn = nxn-1 ddxx =12x

Q: I. Find the derivative of y with respect to x. Use the given relation in its implicit form. d?u 3.…

A:

Q: Find the linear approximation of f(x)=lnx at x=1and use it to estimate ln⁡(1.3) L(x)=? ln 1.3≈?

A: First find the linear equation at x=1  then find the approximate values

Q: Find the approximate value of derivative f(0) with the step size h for the following function by…

A:

Q: 3) Use the definition to find the derivative of f(t) = +1 t+1 %3D

A: f'(t) = -1/t2

Q: Find the derivative of the function. 1 g(x) = dt Jtan(x) V2 +

A:

Q: 4. Find the Linearization of f (x) sinx at a Provide your answer as L(x) =?

A: The given problem is to find the linearization of the given function at given point. Given…

Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A: Given function, fx=e-x a=-0.1 Formula for the linearization at x=a is given by Lx=fa+f'ax-a

Q: 1. F(x) = S, t³ - 5t dt

A:

Q: et dt. · e2t 5. Find and simplify the derivative of f(x) = %3D 1 -2 In z

A: Assume g'(t) = e^t/(1-e^(2t))

Q: Find the gradient of the tangent to the curve xy“ + y+ ( log_(x – 2))² = 14 at the point (3, 2).

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Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: Given: fx=xx+1 We want to find a linearization at a suitably chosen integer near a at which the…

Q: Q2: A) Find an equation of the line tangent to the function of x² + (y-x)2 9 at x 1. dy x-x3 B)…

A: