Find the equation of the curve that passes through the point (7,5) if its slope is given by dy 3D 8х — 2. dx y =

Q: d the equation to the tangent line to the curve y= 4 -r* where x=1.

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Q: find an equation for the line in the xy-plane thatis tangent to the curve at the point corresponding…

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Q: Find the equation of the curve that passes through (0, 9) if its slope is given by dy/dx = 12x^2 −…

A: We can find the equation of the curve by integrating the given derivative and substitute the point…

Q: Find an equation for the line in the xy-plane that is tangent and normal to the curve x³y² + y² = x…

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Q: Find an equation of the line tangent to the curve at the point corresponding to the given value of…

A: Given curve is Firstly, we will find value of x and y at t=3pi/4

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

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Q: Find an equation for the tangent to the curve y = 18 at the point (1,6). 2. X +2 O A. y= - 4x + 10 O…

A: The equation of tangent  y = -4x +10  Hence option (A) is correct

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: 4. Find y'(x) for x²y² – 2x = 4 – 4y. Then find the equation of the tangent line at (2, –2 _n…

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Q: Find the equation of the line tangent to the curve y=t-1 and x= 2t2 at t=2

A: Given: The curves are y = t -1 and x = 2t2 . The value of t = 2   To determine: The equation of the…

Q: 5. Find the equation of the tangent and normal lines to the curve x = t2 – 2t, y= t3 - 3 when t =…

A: Firstly we find Slope of tangent and slope of normal to the given curves and then we will find…

Q: Find the equation of the line which is tangent to the granh of y .3r2 2r + 4 at tho

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Q: Find an equation of the tangent line to the curve y=2x2+3 that is parallel to the line 8x-y+3=0. а.…

A: Topic:- application of derivatives

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

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Q: Find the equation of the tangent to the curve xy2 + y³ = 6x + 3y at (1,2)

A: The curve is given as x y2 + y3 = 6x + 3y, the objective is to find the equation of tangent line at…

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: 2) Consider the curve defined by -8x² + 5xy + y³ = -149 dy a) Find dx b) Write an equation for the…

A: solution is given below

Q: Consider the equation a²y + 3y° = 24, dy a) dx b) Determine the points, if any, where the tangent…

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Q: Given the equation below, find dy dx = Y dy dx - 17x² + 7x68y + y ¹⁰ = - 9 dy Now, use to find the…

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Q: Find the coordinates of the point where the equation y' – xy = 2 has a vertical tangent.

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Q: dy = 18yx³ dx and whose y-intercept is 4. y(x) =

A: A detailed solution is given below

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: Find an equation of the tangent to the curve at the point (1, 81) I = e', y = (t– 9)2

A: Given: x=et,y=(t-9)2   at (1,81)

Q: Find the equation of the tangent line to the curve x =t2 -2, y =t³ -2t + 1 at the point t=2.

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

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

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Q: Find an equation for the line tangent to given curve y = -10z2-3 4r+1 3 at x = 0-

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Q: Can you solve this problem and show all of the steps and say the correct letter

A: here the given equation, we have to find the slope of the tangent at point (1, 1).

Q: Find the equation of the tangent line to the curve x=t2−2t, y=t2+2t at the point t=2.

A: Given equation of curve is Now,

Q: Consider the equation sin(x+y) = 2x-y^2. Find dy/dx and find the slope of the tangent line to the…

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Q: Find an equation of the line tangent to the graph of y sin x – 3y = 4 at the point %3D (, 4) .

A: y2sinx - 3y = 4 at (π/2 , 4) we have to find slope of function 2ysinx(dy/dx) + y2cosx -3dy/dx = 4…

Q: If the line 3x - 4y = 0 is tangent in the first quadrant to the curve y = x^3 + k then what is the…

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Q: (b) Find the equation of the line normal to the tangent at the point x’y+xy² = 6.

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Q: s) Find the equation of the curve that passes through the point (3, 2) if its slope is giv dy = 8x –…

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Q: Differentiate implicitly to find dy/dx. Then find the slope of the curve at the given point. y2 8;…

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

Q: Find the equation of a curve having a slop by dy xy? у 3 ху? —, x > 0 dx and passing through the…

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Q: of the curve yln x + 5x² + y' =13 at the point (1,2) dx b) Find

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

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

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Q: Find an equation of the curve that satisfies dy 33yr10 dx and whose y-intercept is 4. y(r) =

A: The given differential equation of the curve is, dydx=33yx10 Given that, the y-intercept is 4. That…

Q: Find the slope of the tangent line to the given curve at t=-2. Sx=r-1 y=²-28t The slope is

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Q: Find the point(s) on the curve t3 3t, y 2t2 +t 2 x = - where the slope of the tangent line is equal…

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Q: x = 2t + 5, y = t8, t = –1

A: To find the equation of tangent line given x=2t+5,y=t8,t=1

Q: Find an equation of the tangent to the curve r + ry + y² = 3 at (-2, 1). %3|

A: First find the slope of the tangent with the help of derivative of the curve than write the equation…

Q: Find the slope of the tangent line to the curve 2a? – 4xy – 4y³ = 4 at the point ( – 2, – 1).

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Q: Find the equation of the line tangent to y = sin(x) going through 4

A: Given, y=sinx                 ...(1) At x=π4 Put x=π4 in equation (1) y=sinπ4y=22 Thus, the pointπ4,…

Q: 8x^2y^2 = (x^2 + y^2 )^3  Find an equation for the tangent line to the curve at the point (−1, 1)

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Q: nd an equation of the tangent to the curve f(x) = /x+ 8 that has slope %D 4 А. 1 y = X. В. 1 y 7x+3…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.