Find the slope and the equation of the tangent line to the given curve at the point corresponding to the specified value of the parameter. x = t3 + 6t + 1, y = 2t - t2, t= 1 Slope of the tangent line = Equation of the tangent line = Input in slope-intercept form.

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 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: Find an equation of the tangent line to the curve 2(z² + y°)² = 25(æ² – y³) (a lemniscate) at the…

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Q: find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.

A: Given: y=x2-x, P4,-2 We know that for any given functiony=fx slopem of tangent at pointx1,y1 is…

Q: Find the equation of the tangent line at the given point on curve. ex2+ y2 = xe5y - y2e5x/2; (2, 1)

A: Given, ex2+y2=xe5y-y2e5x2:(2,1) To find the equation of tangent line at the given point on the…

Q: Find an equation of the form y = f(x) for a curve with æ-intercept 0 whose tangent line at any point…

A: We have to find

Q: Find an equation of the tangent line to the curve at the given point. y = (1 + 5x)°, (0, 1) %|

A: Given equation of curve: Point (0, 1)

Q: Find the equations of the tangent lines at the point where the curve crosses itself. x = t3 - 5t y =…

A: The gradient of the tangent to a curve at any particular point is given by the derivative of the…

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: Find the equation of the line normal to the tangent at the point (1,2) x’y+xy² = 6. on the curve

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Q: Find the slope of the tangent line to the curve g²y -y = 6 at the point (1, 3). -18/5 0. -3 18 -5/18

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Q: Find the equation of the tangent line to the curve at the given point. y: (6, 1)

A: Recall: Point - slope form : y-y1= m x-x1 ; where , 'm' is the slope and x1,y1 are the given…

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

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Find the equation of the tangent line to the curve at the given point. y = 9x - 8Vx, (1, 1) %3D

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Q: B. Find the slope and the equation of the tangent line to the curve 1. y = 4 - 3x at (- 1, 1) 2. y…

A: We need to find the slope and the equation of the tangent line tothe following curve:3. y=3x2+2 at…

Q: Find an equation of the tangent line to the curve at the given point. y = (1 + 3x)°, (0, 1)

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Q: Find an equation of the tangent line to the curve at the given point    y= xe^-x^2 , (0,0)

A: Given,

Q: Find an equation of the tangent line to the curve at the given point. y = Vx, (64, 8)

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Q: Find an equation of the tangent line to the curve at the point (3, 11). х — 1 y = X - + 9 ·2 y =

A: Note: As per our company guidelines we are supposed to answer the first question only. Kidnly ask…

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

A: Given: To find an equation of the tangent line to the curvey=x at the given point (1,1)

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: 6. Find the equation of the tangent line to the curve r* - a*y" = 12 at the point (-2, 1).

A: the equation of the tangent ( x0, y0 ) to the curve y=f(x) is    y – y0 = f ′(x0)(x – x0)

Q: find equations for the lines that are tangent,and the lines that are normal, to the curve at the…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: a) Find an equation for the tangent line to the curve y= 2/x at the point (2, 1) on this curve.

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Q: Find an equation of the tangent line to the curve y = 9" at the point (1, 10).

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

A: This question is based on application of Derivative.

Q: Find all points on the curve  x 2  y 2 + xy = 2  where the slope of the tangent line is - 1

A: We first find dy/dx using implicit differentiation

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

A: We have given the curve y = x5 + 3e5 and the point (0, 3). Find the slope at x = 0. Therefore, we…

Q: Find the equation of the tangent line to the curve at the given point. y = V2x + I, (4,3) y =

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Q: Find the slope of the curve at the given point P and an equation of the tangent line at P. y = x² +…

A: Let's find

Q: Find an equation of the form y = f(x) for a curve with r-intercept 2 whose tangent line at any point…

A: Here, to find the equation of the curve of the form y=f(x) with x-intercept 2. That is curve passes…

Q: Find an equation of the tangent line to the curve at the given point. y = Vx, (25, 5)

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Q: Find the equation of the tangent line to the curve at the given point. y = 4x^2-x^3, (1,3)

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Q: Find the slope of the curve and equations of the tangent and normal to the curve at the given point.…

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Q: Find an equation of the tangent line to the curve at the given point. y = 2ex + x, (0, 2) y 11

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Q: B. Find the slope and the equation of the tangent line to the curve 1. y = 4 - 3x at (- 1, 1) 2. y =…

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Q: Find the slope of the line tangent to the curve y =x at the point (- 0.4, 0.16) and then find the…

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Q: Find an equation of the tangent line to the curve at the following point: y = (1+ 4x)", (0, 1) y =

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Q: Find the equation of the tangent line to the curve y = (1+2x)² at the point (3, 49).

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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: find the equation of the tangent lines to the curve y=2/(1-3X) at the points with x-coordinates 0…

A: Find the y- values for the given values of x.

Q: Find the equation of the tangent line to the curve y = ex at 0, 1+8 ex What is the equation of the…

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Q: 4. Find the equation of the tangent lines to the curve y = √x and perpendicular to the line 14x +…

A: We have to find the tangent

Q: Find an equation of the tangent line to the curve 2(2² + y?)? = 25(x² – y²) (a lemniscate) at the…

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Q: Find an equation of the tangent line to the curve at the given point. y = √ x,  (81, 9)

A: Given: y=x, (81, 9)

Q: Find the slope of the tangent line to the curve x+y3D6 xy at the point (3,3). (a) 0 (b) -1 (c) 1 (d)…

A: To find: slope of tangent line at the point (3,3) to the equation of curve given below.

Q: Find the equation of the tangent line to the curve y = + 6x at its point of intersection with the…

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

Q: Find the equation of the tangent line at (2,2) on the curve x² + xy + y² = 3

A: Topic = Derivative

Q: Find an equation of the tangent line and normal line to the curve at the given point. y = x* – 2e*,…

A: Given curve is y=x4-2ex. To find the equation of the tangent line and normal line to the curve at…

Q: B. find the slope of the tangent to the curve at the given point 1. y= x-6, (1, - 2) 2. y = 3x -5x.…

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