Consider the curve defined by 2x2 + 3y² – 4xy = 36 dy 2у-2х (a) Show that Зу-2

Q: 1) Find an equation of the tangent line to the curve at (1,1). y = cos (In x²) %D

A: Given. Curve is  Y = cos(ln X²) We need to find the equation of the line which is tangent to the…

Q: 8. Find the equation of the tangent and normal to the curve y = x3 3x + 1 at x = -1. [4] -

A: We have to find the eqution of tangent and normal of given curve y

Q: The equation of the tangent line to the curve at the given point. x² + y2 +3 = (2x+2y + 9x)2, (0, 1)…

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Q: Find the equation of the tangent line to the curve x + y² = 4 where the slope of the curve is 1.…

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Q: 2. Find the equation of the tangent line to the curve at the given point by eliminating the…

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Q: Find the equation of the tangent line drawn to the curve y-4x-6xy 0 at the point (-1,3) O 6x+5y-21-0…

A: Given query is to find the equation of the tangent to the curve

Q: 1. Find the equation of the tangent line to the curve x = e', y = et at t = 1.

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

Q: 12) Find an equation of the tangent line to the curve at t = 2: x = 3t – 5 y = t3 – 6

A: Given data is : x=3t-5y=t3-6 At t=2, x=3×2-5=1y=23-6=2 Therefore point is 1,2

Q: 1. Find the equation of the tangent line to the curve: x = = VE, y = et %3D at t=1.

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Q: b. b. y = 2 1+e-x at (0,1)

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Q: 5. Find the equation of the tangent line on x² + y? = (2x² + 2y² – x)² at (0, ).

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Q: Find the equation of the tangent line on the curve x2 + y2 + 2y=0 at (0, – 2). A y= - 2 B) y= - x…

A: In this question we have to find the equation of the tangent line on the given curve.

Q: (a) Find an equation of the tangent line to the curve y = (1+x²/3}3/2 at x = -1.

A: Given: y=1+x2332 for finding equation of tangent at given pointx=-1, first we need to find slope of…

Q: B) Find an equation of the tangent line to the curve at the given point y = (1+ Vx)³ at x =1 ?

A: Given curve is, y=(1+x3 )3 at x=1.  The objective is to find the equation of the tangent.     For…

Q: Find an equation of the line tangent to the curve y = e at (0,1). 2x

A: We need to find the equation of tangent to the curve: y=e2x  at (0, 1) This can be done as follows:

Q: Find an equation of the tangent line to the curve y = (4x + 2)e at the point a = 0.

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Q: 1) Find an equation to the line tangent to y = (x – 3) 2 at x = 0.

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Q: Find the equation of the tangent line and normal line to the graph of y = x-1 at the x+1 point where…

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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: An equation of the tangent line to the curve y = sin(x) at x = Зп /4 is %3D y = - (х — Зп /4) .

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: 2. Find the equation of the tangent and normal to the curve x = V4t + 1 at t = 2

A: Given the curve :

Q: A) Find the equation of the tangent line to the curve x²y + xy2 = 6 at x = 1

A: Given: The equation of curve , x2y +xy2 =6,  x = 6 To find: The equation of tangent line to the…

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: 3. Find the equation of the tangent to the curve 3xy-y²= 7 at the point (.1).

A: Follow the procedure given below.

Q: 3. Find the equation of tangent line to the curve 2x – y + 3 = 0 x = t – 1, y = t³ + 1 parallel to…

A: Equation of tangent line is given by- y - y1  = m (x - x1)

Q: 13. Find the equation of the tangent line to the curve x'y' + 4.xy = 12y at the point (2,1).

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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: d the equatiom of the tangent line to the curve xy – 7 = Vx + y² at the point (5,2).

A: For finding tangent line to the curve , find the derivative of the function and put the value of…

Q: Find the equation of the tangent line at the given value of x on the curve. y+xy² -22=Dx+5y; x= 5

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Q: 6. Compute and write the slope of the tangent lines to dx y - xy +6 = 0 at the point (5,2). a. b. 2y…

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Q: Find an equation of the tangent line to the curve 2(a2 – y²)² = 25(x² + y²) at %3D (3, 1)

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Q: 46. Show that the sum of the x- and y-intercepts of any tangent line to the curve Vx + Jy = \c is…

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Q: Find the equation of the tangent line to the curve at the point (-÷5) (글 given a cos(2 y) = 0. V3 a)…

A: We need to find the equation of the line.

Q: (a) Find the equation of the tangent line to the curve x = e', y=e %3D at t = 1 without eliminating…

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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: 4. Find the equation of the tangent line to the curve 2xy+r sin y = 27 at the point (1.%).

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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).

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Q: 1. Find an equation of the tangent line to the curve y = Vx at the point (1, 1).

A: Question no. 1Given,            A n equation of the tangent line to the curve y=x at the point…

Q: 1. Find the equation of the tangent line to the following curves at a given point. . y = Vx +3 at x…

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

Q: II FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT THE INDICATED POINT.…

A: We know  ,        The equation of tangent is :              Y - Y1 = m ( X - X1)  The equation of…

Q: 3. Find the equation of the tangent line at point P(2,1) to the graph of the curve f(x) = v3x – 5

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Q: Find the equation of the tangent line on the curve defined by 2xy - y2 = 1 at x = 1. a. y = 1 b. y…

A: To determine : The equation of the tangent line on the curve defined by 2 x y - y 2 = 1   at   x =…

Q: 8. Find the equation of the tangent line to the curve x = In t , y = 1 + t² when t = 1. %3D

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Q: 2. Find the equation of the tangent and normal lines at a given point on the curve. x²y² – 10y + 8x…

A: the equation of the given curve is: x2y2-10y+8x=0 the given point is (2,4) we have to find the…

Q: 1. Find the equation of the tangent line to the curve defined by the equation In(xy) + 2x – y + 1 =…

A: Given: lnxy+2x-y+1=0 for finding equation of tangent at point12,2, we need to find slopem of tangent…

Q: a) Differentiate implicitly to find for the equation x cos y = x2 y2 +1 dx %3D b) Find the equation…

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Q: 2. Find the slope of the tangent line to the curve y? + yx² + x² – 3y? = 0 at the point (0, 3).

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Q: The line y = -4x +b is a tangent line to the curve 3y²r + sin(2y – 4) = /(2y) at (a, 2).

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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: