Linear approximationa. Write the equation of the line that represents the linear approximationto the following functions at the given point a.b. Use the linear approximation to estimate the given quantity.c. Compute the percent error in your approximation,100 | approximation - exact | / | exact | , where the exact value isgiven by a calculator. ƒ(x) = sin x; a = π/4; ƒ(0.75)

Q: g(x) = 1.1x + ex   , (0,1) Find an equation of the tangent line to the graph of the function at the…

A: Equation of tangent line when the slope and points are known: where x1 ,y1 represents the given…

Q: Find all values of x for which f(x) = e?*(x² – 12) has horizontal tangent lines. %3D

A: Horizontal tangent meaning slope of those tangent are zero . Take the derivative and equate to zero…

Q: f(x + h) – f(x) -2h(x + 3) – h? h(x +h + 3)2(x + 3)2 se that . Find the slope m of the tangent lir h

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Q: (viii) Find the equation of the tangent line to the following curve at the point (1, 1). 4.x²y – y =…

A: To find the equation of the Tangent line to the curve at given point

Q: nd an equation of the tangent line to the graph of the function f defined by the equation at the…

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Q: #2.) Calculate the slope of the tangent to the given function at the given point or value of x b.)…

A: 2.b) gx=x+2, P-1,1d) fx=5x-2, P4,52 Note:     multiple questions are given, we are answer only one…

Q: Find all values of x for which the tangent line of f(x) = /x² + 18x+96 is horizontal. A 0,-9 B 0,9 С…

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Q: 14. Let y = 4x² - 4x + 3. (a) Find an equation for the tangent line to this graph at x = 2. (b) Find…

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Q: Find the equations of the tangent line and normal lines to the graph of the function f(x) = -4x – 3…

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Q: (a) Find the point at y = x³ + x, if the slope is equal to 4. Then find the equation of tangent…

A: I have stated the used method in the brackets

Q: (x) = (3x + 1)²; (0, 1) (a) Find an equation of the tangent line to the graph of the function at the…

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Q: a. Determine the derivative of k(x) = (-2x* + 3x - 4)(x" – x- 1). Simplify your answer. b. What is…

A: The detailed solution is given below. Thank you

Q: Find an equation of the line tangent to the graph of f(x) = a) at (1,1); b) a (-37) at a) The…

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Q: 12. Let y = 4x-4x+3. %3D (a) Find the equation of the tangent line to the graph of the function at…

A: Given function is y=4x2-4x+3. To determine: a) Equation of the tangent line to the graph of the…

Q: 3 Find the equation of the tangent line to f- at the point P (-3, 1) for f(x) = :-1 %3D 1- 2x…

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Q: Consider the equation and the given point. f(x) = (x − 3)(x2 + 6),           (1, −14)   (a)Find…

A: Given curve is

Q: a.find the slope of the line tangent to the graph of f at P. b. Determine an equation of the tangent…

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Q: Find the slope m and an equation of the tangent line to the graph of the function f at the specified…

A: Consider the given function: fx=x2x+8 slope of the function is derivative of the function at that…

Q: Step 1 Apply the Definition of Tangent Line with slope m, Ke+ Ax) - Re) x Yr aner cabe underted or…

A: Solution: The objective is to find the slope

Q: Solve the problem. Find where the tangent to the curve f(x) = V+1 that has slope . O x = 3 O x = 1 O…

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Q: C. Provide what is being asked. 1. Find an equation of the tangent line to the graph of y = x* – 3x²…

A: "Since you have asked multiple questions we will solve the first question for you. If you want any…

Q: Fill in the blank/s:

A: point form slope: y-y1=m(x-x1)Where m=f'(x) = slope(x1, y1) is a point on the line.

Q: Answer: 3. Let f(x) = (x³ - 2x)3. %3D (a) Find the slope of the tangent line to f(x) at r = -1.…

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Q: Consider the function f(x) = x³ +1. (a) (2 pts.) Calculate the equation for the tangent line to the…

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Q: Find the indicated quantities for f(x)=2x2.   ​(A) The slope of the secant line through the points…

A: f(x)=2x2 Equation of line having slope m and passing through the point (x1, y1) is given as…

Q: Find the indicated quantities for f(x)=5x2 (A) The slope of the secant line through the points…

A: Given function fx=5x2To find the slope of this secant line , we first need to find the values at…

Q: Find the equations of the two tangent lines to the graph of f that pass through the indicated point.…

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Q: 4x2 Find the values of x where the tangent line is horizontal for the graph of f(x) = x+2 O A. x=0,…

A: Given: fx=4x2x+2 tangent of given expression will be horizontal, where derivative of given…

Q: Find the equations of the tangent line and normal lines to the graph of the function f(x) : -15x + 3…

A: Given that  f(x)=-15x+3  At x=1

Q: 36. Find an equation of the tangent line to the curve at the given point. y = Vx – x , (1,0) - 56.…

A: Given equation y=x14-xDifferenciate with  respective xdydx=14x14-1…

Q: 51. Find an equation of the tangent line to the graph of y = x? + 3/(x - 1) at (a) x = 2; (b) x = 3.

A: The given equation of the curve: y=x2+3(x-1)

Q: Find f'(x) Find f(2) Find f'(2) Write the equation of the tangent line at x=2

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Q: f(x) = x3 + x + 6;    (−2, −4) (a) Find an equation of the tangent line to the graph of the…

A: f(x) = x3 + x + 6Recall the famous rule of differentiation: d(xn) / dx = nxn-1

Q: 14. Find an equation of the line that is tangent to the graph of the function J)= 5x and parallel to…

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Q: 4x? Find the values of x where the tangent line is horizontal for the graph of f(x) = x+2 O A. x= 0,…

A: When tangent horizontal then their slope always equal to zero

Q: Find an equation for the tangent line to the graph of the given function at (4,25). f(x) = x² + 9…

A: Given graph isf(x) = x2+9we have to find the equation of the tangent line at (4,25)we have f(x) =…

Q: 3. Find the equation of the tangent line to the graph of the function at the given point. (a) #61. y…

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Q: a. Find an equation for the secant line through the points where x has the given values. b. Find an…

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Q: Find all values of x at which the tangent line to the curve y = 2x+3 x+1 has the y-intercept 2.…

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Q: Find the indicated quantities for f(x) = 2x. (A) The slope of the secant line through the points…

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Q: Determine the value(s) of x where the slope of the tangent to g(x) = (x+ 5)(x² – 1) is -7. %3D

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Q: Find the indicated quantities for f(x) = 2x². (A) The slope of the secant line through the points…

A: note : According to our guidline i can solve only first 3 , please reroute remaining question.

Q: (a) Find the point at y = x³ + x, if the slope is equal to 4. Then find the equation of tangent…

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Q: Find all values of x at which the tangent line to the curve y = 2x+17 has the y-intercept 2. x+8…

A: This question is related to curve and tangent, we will use differentiation to solve it.

Q: Solve the problem. Find where all tangents to the curve f(x) = that have slope -1. x + O x = 0 O x =…

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Q: et f(x) = 3x 1, 6). 3x? + 6. Find the equation of the line tangent to the graph of y = f(x) at the…

A: Given query is to find the equation of the tangent.

Q: Find the equation of the tangent line T(x) to the graph of the given function at the indicated…

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Q: a) Write the equation of the line that represents the linear approximation to the function f(x) =…

A: (a) Consider the given function as fx=secx and one point x=π4. Find the derivative of the function…

Q: 13x Ca) If F(x) = find F'(3) and use it to find an equation of the tangent line to the curve y = 13x…

A: Given function is : Fx=13x4+x2 To find the value of F'3 and to find the equation of tangent to the…

Q: a. Determine an equation of the tangent line and the normal line at the given point on the curve. b.…

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