Use linear approximatic following questions: (a) Choose a proper function and a value of a; and graph the function and the tangent line to the function at a. Indicate the points on the graph and the tangent line. (b) Find the equation of the tangent line and use it to find an approximation. (c) Without using the calculator, determine if the approximation is lower or higher than the actual value. And explain why.

Q: Find the equation of the tangent and normal line of the function f(x) = 2x – 1 at the point (5, 3).

A: fx=2x-1   First find equation of tangent line of given function  We need to find the slope of…

Q: Find an equation of the tangent line at the given point.…

A: Given, y2ex2-16-xy-1=2Point=4, 2

Q: Find an equation of the tangent line to the curve y=2x^2+3 that is parallel to the line 8x-y+3=0

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Q: Use the definition of a derivative to find the equation of the tangent line at the given point.…

A: The equation of the tangent line is  y-7x+2=0

Q: Find an equation of the tangent line to the curve at the given point. y = 3x3 – x2 + 2, (2, 22) y =

A: Given curve and points are: y=3x3-x2+2  , 2,22

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

A: Slope is derivative of y with respect to x. And equation of tangent is (y-y1) =m(x-x1).

Q: write an equation for the tangent line at the given point x +y = 4, (/2, V2)

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Q: 3. Find the tangent lines and normal lines to the curve y = x4 - 4x3 + 6x2 – 4x + 3 with slope…

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Q: Find an equation of the tangent line to the curve at the given point. y = 3x2 - 12x + 1, (5, 16)

A: Solve by eq

Q: Find the slope and an equation of the tangent line to the graph of f(x) = 2x + sqrt(x) the point (1,…

A: Given line :

Q: Find the equation of the tangent line to f(x)=xe2x-2 + 3 at the point (1,4).

A: Slope of a tangent of a function at a point is equal to the value of the derivative at that point.To…

Q: Write an equation for the tangent line to g(x) at x = 2 if g(2) = 7 and g' (2) =-3.

A: g(2)=7 and g'(2)=-3 , we have to find tangent line

Q: Determine the equation of the tangent line and the normal line to the curve f(x)=x3 -3x2 +2x +2 at…

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Q: Find the equation of the tangent line to the following function at the point given. Use point‐slope…

A: We know that equation of tangent line is ,  y - y0 = m ( x - x0 )  Here m is the slope of tangent…

Q: Find an equation of the tangent line to the curve at the given point. y = 2x3 – x2 + 4, (2,16) y =

A:

Q: Find an equation of the tangent line to the graph at the given point.

A: The given function is fx=27x2+9.

Q: Find an equation of the tangent line to the curve at the given point. y = Sqrt(x) (81,9)

A: Consider the given function:

Q: Find an equation of the tangent line to f(x)=-x – 4x at the point (-1,5).

A: The above question is answered in next step and we can find the equation of the tangent line

Q: ; Find the equation of the tangent and normal line of the function f(x): V2x – 1 at the point (5,…

A:

Q: Find the equation of the tangent line to the curvef (x) = x- + 2x at x = 1. Enter the answer in the…

A: Given: f(x)=x2+2x     at   x=1 To find the equation of the tangent line.

Q: Find an equation of the tangent line to the curve at the given point. X + 1 y = (5, –6) X - 6 y =

A:

Q: y = 3x4 – 8x³ + 6x²

A: Given equation is: y=3x4-8x3+6x2 Applying first derivative test for this equation:…

Q: If f(2) = 3 andf'(2)=-1, find the equation of the tangent line when x = 2 %3D %3D %3D

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Q: Find an equation of the tangent line to the curve at the given point y = 2x3 - x2 + 5, (2, 17) y =

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Q: Find the equation of the tangent and normal line of the function f(x) =√(2x − 1) at the point (5,…

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Q: Find an equation of the tangent line to the curve x^(2/3)+y^(2/3)=13 at the point (−27,−8).

A: Given:

Q: Find the point of tangency and equation of the tangent line of the following functions given a…

A: Given is the equation y=3x+2. The objective is to calculate the point of tangency and the equation…

Q: . Find the equation of the tangent line corresponding to x = 1. (Hint: What y value does this point…

A: Given the equation x2-y3=0 To find the equation of the tangent line at x=1

Q: Find an equation of the tangent line to the curve at the given point. y = 2x2 - 6x + 1, (4, 9) y =

A: First find slope at given value then equation of tangent line

Q: Find the equation of the tangent and normal lines to the curve y=sqrt(x) at the point (1,1).

A:

Q: Find equations of the tangent lines to the curve at the given point: f(x, y) = 4x2+y? 2

A: Given:      fx,y=4x2+y2 at 32,1          4x2+y2=0            y2=-4x2 differentiating on both sides…

Q: Write an equation for the tangent line to g(x) at x = 2 if g(2) = 7 and gʻ(2) = –3.

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Q: Find the equation of the tangent and normal line of the function f(x) = \sqrt(2x−1)​ at the point…

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Q: Find an equation of the tangent line to the curve at the given point.y = x4 + 5x2 − x, (1, 5)y=

A: Equation of the curve: y = x4 + 5x2 − xSLope of the curve = dy / dx

Q: Find an equation of the tangent line to the given curve at the specified point:  y= ( sqrt(x)…

A:

Q: Find an equation of the tangent line to the curve at the given point. y = 2x2 - 8x + 1, (5, 11) y =…

A: To find: The equation of tangent to the curve y=2x2-8x+1 at 5,11. Given: The equation of curve is…

Q: Find the equation of the tangent line with values g(x)= squareroot x and f(x)= x2

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Q: Find an equation of the tangent line to the curve at the point (3, 9). X- 1 y = + 7 X - 2 y =

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Q: Find the equations of the tangent lines of the curve y = that have slope 1+ 2r

A: Given data:   The expression for the curev is: y=2x1+2x. The given slope of the curve is: m=2/9.…

Q: Find an equation of the tangent line to the curve at the given point. y = 3x2 – x³, (1, 2) y =

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

A: Solution :   Given that                      y=x3+x   and The slope is equal to 4 i.e m= dydx=4

Q: If f(x)  = 3x2 -x3, find f'(1) and use it to find an equationof the tangent line to the curve  y=…

A: Given that, y=fx=3x2-x3      ...(1)

Q: Find an equation of the tangent line to the curve at the given point y = x3 - 2x + 2, (2,6) y =

A: From the given data:

Q: Use implicit differentiation to find an equation of the tangent line to the devil's curve,defined by…

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Q: Find an equation of the tangent line to the graph of the function at the given point. y = 5x−2, (2,…

A: Find an equation of the tangent line to the graph of the function at the given point. y = 5x−2, (2,…

Q: Find an equation of the tangent line to the curve x2/3 + y2/3 point (1,8). 5 at the

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Q: Find an equation of the tangent line to the curve at the given point. y = x* + 8x2 – x, (1, 8) y =

A: Given: y=x4+8x2-xPoint (1,8)

Q: Find an equation of the tangent line to the curve at the given point. f(x) = 7x2 - x³, (1, 6) y =

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