Find the linear approximation of the function f(x) = /1 – x at a = 0 and use it to approximate the numbers J0.9 and J0.99. Illustrate by graphing f and the tangent line.

Q: Let f'(a) denote the derivative of the function y = f (x), calculated at x a. Prove that the…

A: Given,                  y= f(x)                      (1)

Q: Find the value of the derivative y′(x) at x=0 for the function given by ey+xy=e.

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Q: Use the intermediate Value Theorem to show that between x = 0 and x = 1, the function f(x) = 3 sinh…

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Q: Let Q(t) = t2. Find a formula for the slope of the secant line over the interval [1, t] and use it…

A: the slope of the secant line over the interval [1, t]   For slope of the tangent line, replace t…

Q: Consider the function f(x, y) = y³ – 2y – x². Find the direc- tion of greatest increase at the point…

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Q: Use linear approximation to approximate v25.1 as follows. Let f(x) = Vx. The equation of the tangent…

A: equation of tangent line is :  y - y1 = m ( x - x1 )  here m is a slope and ( x1 , y1 ) is a point…

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(r) = V9r +…

A: Given:       fx=9x+5 at x=1  Instantaneous rate of change :    If y=fx, the instantaneous rate of…

Q: Use linear approximation to approximate v81.4 as follows. Let f(x) = Vx. The equation of the tangent…

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Q: Find the line tangent to the graph of f(x) = cos(x) at xo = T.

A: f(x)= cos(x)  Then, f(π) = cosπ⇒f(π) =-1

Q: QIFind the derivative of the function f(z, k) = z* – 16k + tanh(z) – 4 csc(k) in terms of z and k ?

A: Dear student  Here is the solution of your query

Q: The current in a wire is defined as the derivative of thecharge: I(t)  =Q'(t). What does  ∫ab I(t)…

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Q: Use the Product Rule to compute the derivative: d. Find dt (e + 1)(t + 9)) at t = 13

A: Topic :- Derivative

Q: + (z), V1– 2z y =1- cos (z) + /1 – 2z

A: Given : y = xcos-1x+1-2x

Q: Let f(x, y) = V xy. Find the derivative of f. af 1 ду 2

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Q: Use the Fundamental Theorem of Calculus to find the derivative of y- " cos t dt t12

A: Given that  y=∫-9xcos tt12dt

Q: Consider J(0) = 30* + 1. Let e = 0.001, compute the numerical approximation to the derivative at 0 =…

A: The given problem is to find the derivative of the given function at point 2 with given accuracy…

Q: Compute forward difference approximations for the first derivative of the function, y =[ eln(x)2, at…

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Q: find the derivative of the function at P0 in thedirection of v. ƒ(x, y) = 2xy - 3y2, P0(5, 5), v =…

A: The given function is ƒ(x, y) = 2xy - 3y2. Note that fx=2y    and  fy=2x-6y. at P0=5,5,  fx=10   and…

Q: Use the Product Rule to compute the derivative: Find d/dt ((t^2+1)(t+9)) at t=5

A: To find  ddt[t2+1t+9]    at t = 5 Using Product Rule of Derivatives

Q: Let f(x) = 2x³ – 9x² – 24x + 19 A. Differentiate f. B. Determine the values of r , if any, at which…

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Q: Find the derivative. F(t) = In(sinh(2t)) %3D F'(t) %3D

A: Find the derivative of the function

Q: Find the derivative of the function. r sin(x) y = Jcos(x) In(4 + 9v) dv y'(x) = %3D

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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: . Use the forward-difference formula to approximate the derivative of f(x)= Inx at x, =1.9 using…

A: Forward Difference: For small values of h, the difference quotient can be used to approximate with…

Q: Use the Product Rule to calculate the derivative.

A: y=t-8t-1et+t2

Q: Find the derivative of the function. s = t In |t| ds dt 11

A: The objective is to find the derivative.

Q: Use the Quotient Rule to compute the following: d ( t2 +1 at t = -4 %3D dt \ t2 – 1 The derivative…

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Q: Use linear approximation to approximate v25.1 as follows. Let f(x) Vx. The equation of the tangent…

A: The given functin f(x)=x at x=25

Q: Evaluate the derivative dt -for the function y = 4vī cosh vĩ – sinh(t²).

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Q: What is the difference between the linearization, L(x), of f at a, and the linear approximation (or…

A: Given question:- What is the difference between the linearization, L(x), of f at a, and the linear…

Q: Find the equation of the tangent line T to the graph of f at the given point. Use this linear…

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Q: The slope of the tangent to the curve f (x) = 2" at x = 1 is approximately (to three decimal…

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Q: Consider a function defined implicitly as 7x + y² = cot y. Find the gradient of a tangent line at a…

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Q: Use linear approximation to approximate v81.4 as follows. Let f(x) = Vx. The equation of the tangent…

A: Consider, fx=x Differentiating with respect to x, we get f'x=12x Now slope of the tangent line at…

Q: Use linear approximation, i.e. the tangent line, to approximate V27.3 as follows: Let f(x) = Vx. The…

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Q: I. Determine the equation of the tangent line to the graph of f(x) V3+ 5t5 dt at I= 1.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find the equation of the tangent line T to the graph of f at the given point. Use this linear…

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Q: Differentiate the function and the function of the tangent line at the given value of the…

A: Given, s=t^3-5t^2 t= 3

Q: Let F(x) = dt. Find an equation of the tangent line to the curve y = F(x) at the point with…

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Q: Use the Quotient Rule to compute the following: d t2 +1 dt t2 – 1 The derivative is:

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Q: The derivative of the function y = sin VE at a = is equal to %3D 4 14

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Q: Find the equation of the tangent line T to the graph of f at the given point. Use this linear…

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Q: Compute the derivative of h(sin(x)) at x = T/6, assuming h'(0.5) = 10:

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Q: Find the derivative of the following function (2t – 1)* dt F(x) = using the Fundamental Theorem of…

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Q: Find the second of the finchion, ç x) = cos e derivative f (x) (x %3D %3D

A: Consider the given function: f(x)=xcosx The first derivative is calculated using the product rule.…

Q: Use linear approximation, i.e. the tangent line, to approximate V27.2 as follows: Let f(x) = Vx. The…

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Q: Find the equation of the tangent plane to f(x,y)=√2xy+ 1 at the point            (2, 2),and use it…

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Q: Calculate the error of approximation with Ea for the following functions when x = 2, Ax = dx = 0.08

A: If the input of a function y=f(x) changes, its output also changes. The derivative of a function is…

Q: Find the equation of the tangent plane to z = e + x + x² + 4 at the point (3, 0, 17).

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