The graph of f(x) = −sin x has infinitely many tangent lines that pass through the origin. Use Newton’s Method to approximate to three decimal places the slope of the tangent line having the greatest slope.

Q: Find the equation of the tangent line to the curve y = 8 ln(x – 63) at the point (4,0). y =

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Q: Find the equation of the tangent line at the given value of x on the curve. 2y' +xy - y = 54x*, x= 1…

A: Explanation: Given that: 2y3+xy-y=54x4 x=1 Concept: The standard equation of tangent line y=mx+c…

Q: Find equation of the tangent line to the curve y = v2x + 1 at the point (4,3).

A: Given:    y = √(2x+1)  Point (4,3)

Q: Find the slope of the line tangent to the graph of f(x) = xe* at x = 0. %3D

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Q: Find the point where the tangent line to y=x2 at x=0.4 crosses the x-axis. x-intercept =

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Q: Find the slope of the tangent line to the curve of y = x 2 at the point where x = −6

A: Slope of the tangent line is the derivative of the given curve at the given point. So…

Q: -1 Where on the curve y = (256+ x²)¯* does the tangent line have the greatest slope? NOTE: Enter the…

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Q: The slope of the tangent line to the curve y=2eUXcos(-6x) at x-0 is

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Q: 8. Find the point of the graph of f (x) = xe-2x where the tangent line is horizontal. %3D

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Q: Find the point where the tangent line to y = x* at x 0.3 crosses the x-axis. x-intercept =

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Q: Find the slope of the tangent line to the curve defined by 4x + xy – y* 1760 at the point (8, –4). e…

A: To find the slope of the tangent line to the given curve at the given point

Q: Where on the interval [0, 4] does ƒ(x) = 4x - x2 have a horizontal tangent line?

A: Determine the value for derivative of f(x) i.e f'(x). fx=4x−x2f'x=ddx4x−x2=ddx4x−ddxx2=4×ddxx−2xSo,…

Q: 3. Find the equation of the tangent line to the curve f (x)= (1+2x)'" at the point (0,1) in…

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Q: The tangent lines to the graph of f(x) =x² grow steeper as x in- creases. At what rate do the slopes…

A: Given function is, f(x)=x2

Q: Find the equation of the tangent line to the curve f(x)=x9 ln(x2) at x = e. (Do not approximate)

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Q: The tangent lines to the graph of f(x) = x2 grow steeper as x increases. At what rate do the slopes…

A: The tangent line of any given function is the line which  touches the curve of function at only one…

Q: At what point on the interval (0, 7/2) does the tangent line to the curve = 3x + V3 cos x – sinx…

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Q: Find the slope of the tangent line drawn to the graph of −4x^2−xy+3y^3=−200 at the point (−1,−4).…

A: Given function is : -4x2-xy+3y3=-200 To find out slope of tangent dydx at -1,-4 Differentiating…

Q: 2. Find the slope of the tangent 2 line to the curve f (x) = - = -1 at x

A: topic - slope of tangent line to curve

Q: Find the equation of the tangent line at the given point on curve. x2 + y2 = 25; (-3, 4)

A: Given: x2 + y2 = 25; (-3, 4)

Q: The slope of the tangent line to a curve at any point is (5x² - y) ex+y If the curve passes thru…

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Q: Find the slope of the tangent line to the curve defined by 4x + xy – y = 1760 at the point (8, –4).…

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Q: The slope of the tangent line to the curve x^3 + y^3 = 6xy at the point (3,3) is

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Q: Find the equation of the tangent line to the curve y = 8/x2 + x + 2 at x = 2.

A: Given, y=8x2+x+2,  at x=2 slope of curve at x=2 is dydx dydxx=2=-82x+1x2+x+22dydx=-4064=-5/8 at x=2,…

Q: Find the equation of the tangent line at the given value of x on the curve. 3 4 2y° + xy - y =…

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Q: Find the points on the graph of y = ex where the tangent line has slope 4.

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Q: Find the equation of tangent line to the curve at the given point x2 + 2xy - y2 + x = 2 (1, 2)

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Q: Find an equation of the tangent line to the curve  y = xsqrtx  that is parallel to the line  y = 6 +…

A: Given data: *The equation of the curve is y=x×x *The tangent line is parallel to the curve y=6+3x…

Q: Find the exact value of the slope of the tangent line to the graph of 3x2+xy−3y3=1 at the point…

A: The slope of the tangent to a curve y=fx at a point x1,y1 is defined by the formula, Slope of the…

Q: Find the equation of the tangent line to the graph of f(x) = x² – 4 at the point (3, 5). -

A: The equation of the line passing through the point (x1,y1) having slope m is given as (y-y1)…

Q: Find the slope of the function F(x) = √√x+1 at the oint (8,3) And find the equation of the tangent…

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Q: Find the equation of the tangent line (in point-slope form) to . 2 f(x) = 3 – 2x' + In(5x + e) at x…

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Q: 4. Find an equation of the tangent line to the curve x – 1 | at the point (3, 2). ||

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Find the equation of the tangent line at the given point on the curve. 3y-x = 8, (16,2) %3D

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Q: 2) Find the tangent line to y2 = x at the point (4, –2).

A: Given: y2=x…

Q: Find the equation of the curve at every point in which the tangent line has a slope of z2, which…

A: Given slope of the tangent line has a slope of x2. To find equation of curve having slope of tangent…

Q: Find the slope of the tangent line to the curve y = (1+ 4x)7 at the point x = 2. %3D

A: Slope of the tangent line is obtained by just derivative of the function  wrt the independent…

Q: The slope of the tangent line to √x+y+√√xy = 2y at the point (2,2) is:

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Q: Find the slope of the tangent line to the curve f(x) = at the point where x = 9. %3D

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Q: Show that the tangent line to the curve at y = 3x²+ 6x− 5 the point (−1. −8) is horizontal.

A: To show: That the tangent line to the curve at y=3x2+6x−5 the point -1,-8 is horizontal. Concept…

Q: Find the equation of the tangent line on the function f(x) = arctan (x²) at the point (1,).

A: We can find the equation of tangent line to the curve as below.

Q: Find the equation of tangent line to the curve f(x) = x² at x = 3.

A: Topic = Derivative

Q: The tangent lines to the graph of f (x) = x2 grow steeper as x increases. At what rate do the slopes…

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Q: The slope of the tangent line to the graph of xy = In(x² + y²) at the point (1, 0) is

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: Determine the slope of the tangent line to the curve (x² + y² – 2x)² = 2(x² + y²) at (2, 2).

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Q: Find the slope of the tangent line to the curve defined by 6x5 + 8xy +y2 = -13 at (-1,1). The slope…

A: The slope of tangent line to the curve f(x,y)=0 at (a,b) is the value of dy/dx at (a,b)

Q: 3. Find the equation of the tangent line to f(x) = 2x · sin (x) at the point (5, ).

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Q: Find the equation of the tangent line to the curve y = 2 In(x³ – 26) at the point (3, 0). y =

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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: