Find the linear approximation L(x) of the function f(x) = /4 - x at a = 0. L(x) = Use L(x) to approximate the numbers V3.9 and V3.99. (Round your answers to four decimal places.) V3.9 x V3.99 x Ise technology to graph f and the tangent line in the same viewing window.

Q: Find the orthogonal trajectories of the family of curves y=Ce* +10

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Q: find the orthogonal trajectories of the family of curves x2+y2=a2

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Q: .) What is the inner and the outer functions? b.) What is the derivative o

A: Given : The function is f(x) = x2+ 3x +1 .

Q: Q2: Given the derivative f'(x) = x²(x³ - 3), find: (a)The critical points. (b)The stationary points.…

A: Given the function

Q: 4. Find the orthogonal trajectories of the family of curves y= Ce“ + 10

A: Here we have to find the orthogonal trajectories

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

A: Given, f(x)=1x, a=0.9 now find linearization f(0.9)=10.9=109 so linearization at 910,109…

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 error propagated from the function y = 3x* if an error of 0.06 occurs in the independent…

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Q: Find the error propagated from the function y = x³ if an error of 0.05 occurs in the independent…

A: For a function y=f(x) If  error in y is ∆y when error in calculating x is ∆x dydx=∆y∆x

Q: Find the derivative of the given function from the first principle ax2+bx+c

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Q: a) Show that if y = V1 + sin x then =: %3D b) A manufacturer estimates that x units of a particular…

A: NOTE: Refresh your page if you can't see any equations. . the demand function is  the revenue…

Q: doy= Ax²+ B Find the differential of the curve family.

A: Given curve is                                                    lny=Ax2+B we have to find the…

Q: Q2/ Find the orthogonal trajectories of the family of curves x-y - c² YAS

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Q: b) Find the derivative function of f(x) = √5x - 1 using first principles.

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Q: Q2/ Find the derivative of the function f(x) = V3x +1 by definition %3D

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Q: Fill in each blank so that the resulting statement is true.

A: The slope of the tangent at a point on the curve is equal to the value of the derivative of the…

Q: Find f(x) if f(2) - 2x 3 and the tangent line at x has slope (x – 1)e* %3D f(x) =

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Q: Find the function with derivative f'(x) = e8 that passes through the point P= (0,7/8).

A: We are given a diierentrial equatrion[f'(x)=e8x ] and a pssing point (0, 7/8) of the same  we need…

Q: Find the critical point of the function f(x, y) =-(8x+2y2 +ln(|x+y|)). c = Use the Second…

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Q: %3D Apply the Chain Rule to find the tangent line to f(x) = 4v2x- 6e2-*at x = 2

A: We want to find the tangent of the given function at x=2 We know that slope of the tangent at a…

Q: gives the first derivative of a continuousfunction y = ƒ(x). Find y″ and then use Steps 2–4 of the…

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Q: Bus Econ 5.2.47 Tutoring On a particular day, the power used in a particular state (in thousands of…

A: We use second derivative test to find out where function maximum and minimum

Q: 4. Find the orthogonal trajectories of the family of curves y = Ce* +10

A: Given that : y = Ce2x + 10

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

A: The nearest integer to a=-0.9 is -1 because at this point, we can easily find the function's value…

Q: A. Find the derivative of the given function at a given number 1. y =3x -2 at f(1)

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Q: A quadratic function f(x) = x + 3 x2 + 2 x + 3 has an inflectional tangent y = 3 x + 3 at (0,0).…

A: Given:- A quadratic function f(x) = x3+3x2+2x + 3 has an inflectional tangent y = 3x + 3 at (0, 0).…

Q: a)Use the second derivative test to determine whether the function has a local maximum or local…

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Q: Find the error propagated from the function y = 3x* if an error of 0.04 occurs in the independent…

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Q: Suppose the linear approximation for a function f(x) at a = 3 is given by the tangent line y -2x +…

A: The given functions are

Q: Find the critical points for the following function. Then use the second derivative test to…

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Q: Solve for the derivative of the given functions using the Chain Rule formula. Let f(x) = √(x2 + 3x +…

A: (a) fx=x2+3x+1 Inner function : u=x2+3x+1. Outer function : y=u.

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

A: find a linearization at a suitably chosen integer near a.

Q: 1. Find the linear approximation Using this linear approximation, 9.1. of f(x) x^(1/2) at x = 9.…

A: The linear approximation: L(x) for a function f(x) at x=a is defined using the formula:…

Q: How can a linear approximation be used to approximate the value of a functionf near a point at which…

A: Given that the linear approximation.

Q: Verify the given linear approximation at a = 0. Then use a graphing calculator or computer to…

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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: Find the slope of the curve at a given point. (The general process). y^2=3x+1 at (1,2)

A: Using formula for slope of curve.

Q: 4. Find the orthogonal trajectories of the family of curves y= Ce“ +10

A: Given that, Family of curves is following, y = Ce2x + 10…

Q: Use a graphing calculator or computer to verify the given linear approximation at a = 0. Then…

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Q: Assume that it costs Apple approximately C(x) = 36,100 + 100x + 0.01x² dollars to manufacture x 32GB…

A: We use second derivative test to find out where cost is minimum

Q: Q.5 Show that both of the functions f(x)=(x-1)" and g(x)=x' – 3x +3x-2 have stationary points at x =…

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Q: Find the orthogonal trajectories of the family of curves x2+y2=a2

A: We have to find the orthogonal trajectories of the family of curves x2+y2=a2.

Q: Exercise 25. For which x- values does the graph of y = e3a-2a²-4x has a horizontal tangent line?…

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Q: a derivative computation using the FTC and the chain rule t): df 13

A: Given : ddxFx3 =ddx∫13x3e-t2dt

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. (If…

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Q: Q 1. a) Let y = x® – 5x³ + 5x* – 10. Then find minimum and maximum values. b). By using definition…

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Q: Estimate v16.3 using the linearization L(x) of f(x) = /x at a = 16. (Use decimal notation. Give your…

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Q: (a) Show that the derivative solution of this function y = x** is dy = xa*x-1) [1+x In x (In x+ 1)…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: