For the equation given below, evaluate y at the point (1, 2). ev + 10 – e² = 2x² + 2y². y at (1, 2) = Find an equation of the tangent line to the curve x213 + y13 = 5 (an astroid) at the point (8, 1). y =

Q: Find the equation of the line tangent to the curve xy^3+xy=6 at the point (3,1). When the equation…

A: Firstly, we will find derivative And then we can solve for y'and we get

Q: Find the equation of the tangent line to the curve (a lemniscate) 2( +y) = 25(x - y) at the point (-…

A: 2(x2+y2)2=25(x2-y2)2(x4+y4+2x2y2)=25x2-25y22x4-25x2=-25y2-2y4-4x2y22x4-25x2=-25y2+2y4+4x2y2different…

Q: consider the curve given by the equation x^3 - 2xy + y^3 = 0. Find the tangent line of this curve at…

A: Given equation is x3-2xy+y3=0..........(1) we have to find the tangent line of this curve at (1,1)

Q: Find the equation of the line that is tangent to the curve y = 4x cos x at the point (T, -47). The…

A:

Q: Use the implicit derivation to find the equation of the line tangent to the curve at the point…

A: Here, the equation of the given curve is: y sin (2x)=x cos(2y)...(1) To use the implicit derivative…

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: 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: Find the equation of the tangent line to the curve (a lemniscate) 2(x^2+y^2)^2=25(x^2−y^2) at the…

A: Given: 2x2+y22=25x2-y2 at point -3,-1

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: The curve y=ax^2+bx+c passes through the point (1,9) and is tangent to the line y=3x at the origin.…

A:

Q: Find an equation of the line tangent to the curve xy + 4y = 68 at the point (1,16). An equation of…

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Q: The curve y = ax2 + bx + c passes through the point (1, 2) and is tangent to the line y = x at the…

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Q: (b) Find the equation of the line normal to the tangent at the point (1,4) on the curve x'y+ xy =…

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Q: Find an equation of the tangent to the curve at the given point by both eliminating the parameter…

A: Explanation of the solution is given below..

Q: 1) Given the curve 2x? + y3 = x3 + y? find the x-intercept of the tangent line at the point (2,1)

A: We find dy/dx using the implicit differentiation and we plug x=2 and y=1

Q: Consider the following curve. 1 + x y = 4 + ex Find y'(x). -ex + 4 (4+ e*)² y'(x) = ot2 1 Find an…

A: According to the problem, we have

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 the equation of the tangent line to the curve y 3x cos x at the point (T, -37). || The equation…

A: Formula for finding the equation of a line having a slope of m and passing through the point (x1,y1)…

Q: 6.) Find the equation of the tangent lines at the point where the curve crosses itself x = t³ – 6t,…

A:

Q: Consider the following curve: x? + y2 - 4x = 8xy² +92 An equation of the tangent line to the curve…

A: Our Aim is to find an equation of the tangent line to the curve given by:-x2+y2-4x=8xy2+92 -(i) at…

Q: For x/y + 5x - 7 = (-3/4)y, (1,2), find the equation of the tangent line to the graph of the given…

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Q: Q3. Find the equation of the tangent line of the curve y= sinz + cos z at the point A(-, V2).

A: The given curve is y=sin x+cos x and at the point is Aπ4, 2  To find the equation of the tangent the…

Q: Find an equation of the tangent to the curve at the given point by both eliminating the parameter…

A: Tangent line

Q: Find an equation of the tangent to the curve at the given point by both eliminating the parameter…

A:

Q: Find the equation of the tangent line at the point (−2,2) to the curve defined implicitly below. 4y2…

A: We have to  find tangent line to curve at given point at (-2,2).Cirve equation is given by:

Q: Determine an equation of the tangent line to y = (e +2)ª at the point (0, 81), then solve it for y.…

A:

Q: Find the equation of the tangent line to the curve y = 4x cos x at the point (, - 4). The equation…

A: We can answer the question in the following steps.

Q: Find an equation of the tangent plane to the graph y = x² + 2xz at (1,3, 1). (Possible Answer: 4r –…

A: We have to find an equation of the tangent plane to the graph y=x2+2xz at 1,3,1.

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

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Q: 1. For y=In2x, determine the equation of a tangent line parallel to 2x-3y+1=0.

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Q: Find the equation of the tangent line to the curve y = 2x cos x at the point (T, -27). The equation…

A: Using formula of equation of tangent.

Q: Find the equation of the tangent line to the curve (a lemniscate) 2(x² + y²)² = 25(x² – y?) at the…

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Q: II. Find the equation of the tangent line to the curve z2+V#j+y² = 19 at the point (1, 4).

A:

Q: (2.;v3). 1 Find the equation of the tangent line to x? +y²: = 1 at Use exact values in y = mx + b…

A:

Q: Consider the curve given by y2 + (1+x³)3 = xy + 8. Find the equation of the tangent line to the…

A: To find the equation of line tangent to the given curve at point (1,1)

Q: 8. Consider the curve given implicitly by -x2 + 3xy+2y² = 2 y. 8.1. Verify that (1, –1) lies on the…

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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: Find an equation of the tangent line to the curve y = 3 arccos (1,4 π). Select the correct answer.…

A: Find an equation of the tangent line to the curve y= 3cos-1(x/2) at the point (1,4π) .

Q: Find the equation of the tangent line to the curve y = 8 sin z at the point (, 4). 6

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Q: The equation for the tangent to the curve y = t+ at the point (1,3

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Q: The equation of the tangent line to the curve x2 + y? = 25, at (8,-12) is. %3D 8. (x +8) + 12 12 y =…

A: differentiate equation with respect to x. 2x+2y(dy/dx)=0 (dy/dx)=-x/y so, m=(dy/dx)|(8,-12)…

Q: The equation y2(y² – 4) = x²(x² - 5) is known as the devil's curve. Give an equation for the tangent…

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Q: 2. Find the equation of the tangent line to the curve defined by the equations: x(t)=t?-3,y(t)=2t-1,…

A:

Q: 2. Consider the curve given by 3y2 – 2x²y³ +2x +9 = 0. Write an equation for the tangent line to…

A: The given curve is, 3y2-2x2y3+2x+9=0 The slope of the tangent curve is given by dydx Determine the…

Q: Find the equation of the line tangent to the curve xy3+xy=20 at the point (10,1). When the equation…

A: It is given that, the equation of the curve is xy3 + xy  = 20. Use implicit differentiation to…

Q: The equation of the tangent line to the curve r +ỷ = 64, at (5,-13) is (+5) + 13 13 y = 5 (т - 5) -…

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Q: Consider the curve given by y2 + (1+x³)³ = xy + 10. Find the equation of the tangent line to the…

A: Considering the curve- y2+1+x33=xy+10 Firstly, find the slope of the curve. dy/dx is the slope of…

Q: Find the slope of the tangent line to the curve y = g²+4r+7 at the point (0, 3). 7a+2 Determine da…

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