The families of curves represented by the solution of the equation dy dx for n = - 1 and n = + 1, respectively, are

Q: . Find an equation of the line tangent to the curve y = 2 + sin(rx) at a = 1.

A: Given curve is y=2+sinπx at x=1 findequation of line tangent to the given curve

Q: What is the equation of the line tangent to the curve ev + cos(x) = 1 at the point (,0*? Y = 0 A B…

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Q: (a) The curve with equation y 2   = x3 +3 x 2  is called theTschirnhausen cubic. Find an equation of…

A: We find dy/dx at x=1 and y=2  So the slope of the tangent = 9/4

Q: Show that the slope dy/dx is defined at every point on the graph of 2y = x² + sin y.

A: Given- 2y=x2+sinx To prove- That the slope dydx is defined at every point on the graph of the above…

Q: Given the equation below, find dy dx - y = 63x² + 140x69y 2x70+ 5y⁹ dy dx 5,9 ZY Now, find the…

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Q: Consider the curve defined by x2y + 3x + y2 = 38. a. Find dy/dx dy dx .   b. Find an equation of…

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Q: (a) The curve with equation y 2   = x3 +3 x 2  is called theTschirnhausen cubic. Find an equation of…

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Q: Suppose a curve is defined by: x/x-y=y2-1 FIND dy/dx

A: Given curve is xx-y=y2-1 Divide rule of differentiation state as: ddxuv=vddxu-uddxvv2…

Q: find an equation of the curve that satisfies (dy)/(dx)=45 yx^14 and whose y-intercept is 2 y(x) =

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Q: Given that dy dx when x-2 for the curve y=x3- 2x2 – 4x d2y Find and hence find which of the…

A: We have to find the second derivative of given function at x=2.

Q: Use a computer algebra system to plot y2 = x 3 - 4x for x and y between -4 and 4. Show that if dx /…

A: y2=x3-4x

Q: The curve C with equation y = f(x) passes through the point (1, -3). Given the following, find f(x)…

A: We know, ∫xndx= x(n+1)/(n+1)

Q: Find the exact length of the curve. y = Vx - x2 + sin

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Q: Find the equation for the curve f (x) at the point (x, y) meet the following conditions dy / dx = 4x…

A: A curve is a function with equation of the form y=f(x). A differential equation is an equation in…

Q: ,4 Consider the curve whose equation is x4 + y* + 3xy = 5. The dy slope of the tangeant line, at the…

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Q: r = -1 + cos 0 0=t/2

A: In the question we have to find the slope of function -…

Q: Determine dy/dx, if the curve is described by the equation 4y^3-5x^2y=4x^2

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Q: An equation of the line tangent to a curve at the point (1, 3) is y = x+2. If at any point (x, y) on…

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Q: The function f(x, y) = sin(/3x2 + 3y² ) corresponds to plot [ Select ] level curve [ Select] >

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Q: For the implicitly defined curve: cos(7y) 5y sin(x) dy (e.g., find y' ). dx a. Find a formula for dy…

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Q: Find the values of a and b for the curve x2y + ay? = b if the point (1,1) is on its graph and the…

A: The slope of the tangent 'm' at a point (x1,y1) for a curve S(x,y) Is given by dydxx1,y1 therefore…

Q: What is the equation of the line tangent to the curve e + cos(x) =1 at the pointG.0) A (B) y=x+ C…

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Q: Given the graph of r sin 2y = y cos 2x pictured at right, what is the point-slope equation for the…

A: The derivative of the function y'=dydx is the measure of how fast the function is changing with…

Q: 50 Find the length of the curve whose equation is given by r = e on 0 < 0 < 2T.

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Q: #1 Find the equation of the tangent line to y:R @ x- -4 Provide answer in point-slope form dy %3D

A: Differentiate at given point then use equation of line

Q: find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: Given equations - x = sec2t-1                                       x = tan2t         .........(1)…

Q: Find the lengths of the curves y = sin -1x - √(1 - x2), 0≤ x ≤ 3/4

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Q: The curves y = In x and y = 3x² have parallel tangent lines at x = A) ± √/ B) C) √6 E) 2

A: Two lines have parallel tangent if slop at the point is same.

Q: Give the equation of the tangent line to the graph of 3sin y – In(e sech r) = tan-'(x²y) + 3 at the…

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: If -3=-y^2+xy^2-x^2 and it is known that dy/dx=(y^2-2x)/(2y-2xy), find all coordinate points on the…

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

A: The equation of the given graph: x23+y23=5

Q: 1. Given the equation of tangent to the curve y = x³ - x² – 7x + 10 at the point (a, b) is y = 5x +…

A: We know that the equation of the straight line that passes through the point (x0, y0) with finite…

Q: At the given point, find the line that is normal to the curve at the given point. 6x <y - TT Cos y =…

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Q: What is the equation of the line tangent to the curve e+cos(x) =1 at the point ,02 + cos Ay= y=x-…

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Q: Find for the curve dx In (2x) + 5xy + y = 3.

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Q: A curve is defined implicitly by the equation x²+xy+y? =1 dy Differentiate implicitly to find dx

A: here we use basic differentiation form.

Q: Find the equation of the family of curve having the given slope, and the equation of the family…

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Q: Which of the following could be used to find the slope of the line tangent to the curve sin-(2x? +…

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Q: If the length of the curve y = 4 x7 from the point (0, 0) to the point (Xo, f(xo)) is L= 1 (145)*…

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Q: The slope of the tangent line to the graph of y =; I+1 when x = 1 is %3D %3D - 4 3/4 O 1 4. 1/2

A: y=xx+1 Slope of the tangent line is the derivative of the given function at the given point. So…

Q: Find dy/dx and d2y/dx2. x = cos(2t),    y = cos(t),    0 &lt; t &lt; π   For which values of t is…

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Q: Find the values of a and b for the curve x2 y + ay2= b if the point (1,1) is on its graph and the…

A: Find the slope of tangent line

Q: The curve y = sin'x has a slope of %3D Select one: a. at æ = ± O b. Never O c. at x = 0

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Graph the curve over the given interval together with its tangent at the given value of x. 37 19) y…

A: csvs

Q: Find the equation of the tangent to the curve y = x+2x3 through point ( 8,12 ). a. 7x – 6y + 14 = 0…

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Q: 3 If the length of the curve y = 4 xž from the point (0, 0) to the point (xo, f(xo)) is L = ((20737)…

A: Given,          The length of the curve y=4x32 from the point 0,0 to the point x0,fx0           is…

Q: The exact value of the slope of the tangent line to the graph of the curve r = 7 + 8 cos(0), at e =…

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Q: The curve with equation y= e* In(x- 1) has a stationary point when x = p. (i) Show that p satisfies…

A: Given- The curve with equation y = e-2x lnx - 1 has a stationary point when x = p. To Show- Show…

Q: 2- find dy/dx ex = sin (x + 4y) 3-find an equation for the line tangent to the graph f(x) = x - 2x?,…

A: 2. Given function is: e2x=sinx+4y Differentiating with respect to x we get,…

Q: The f '(x) of the given curve is equal to -4 y = sin 3x ||

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