4- Find the length of the curves in Exercises . 1. y = (1/3)(x² + 2)³/2 _from x = 0 to x = 3 3. x = (y³/3) + 1/(4y) from y = 1 to y = 3

Q: Calculate the length of the tangent line, normal line, sub-tangent and subnormal from: a. xy² = 18…

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Q: 5. Find the slope of the tangent line to the curve y + 2yx3 - x-5y3 = 0 at (0, 5). %3D

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Q: Find the equation of the tangent line to the curve y= (1+2x)2 at the point (2, 25). y = %3D

A: This question is based on application of Derivative.

Q: 25. Find equations of all lines having slope −1 that are tangent to the curve y 1/(x − 1). = 1/4…

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Q: Find the length of the arc of the curve 9y2 = 4x3 from the origin to the point (4,). %3D

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Q: Show that the point (2, 4) lies on the curve x3 + y3 - 9xy = 0. Then find the tangent line and…

A: Given: f(x, y) = x3 + y3 - 9xy = 0 To find:  Equation of tangent and normal to the curve at point…

Q: Find the length of the arc of the curve 9y2 = 4x3 from the origin to the point (3,2v3).

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Q: Find length of arc of the curve 9y2=4x3 from the origin to the point (3, 2√3)

A: Given curve is 9y2=4x3, and the point is 3,23.   The objective is to determine the length of arc of…

Q: What is the length of the curve y= x3/2+4 from the point (1,5) to (4,12)?

A: Arc length is defined as the distance between two points on the curve. It is done in such as way…

Q: 5. Hance sits at one of the points on the curve y = 2x³ -3x²-12x +20 where the tangent is parallel…

A: Please see the below picture for detailed solution.

Q: 9. Find the equation of tangent and normal for the curve xsin2y = ycos2x at 4'2

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Q: 2) Find and sketch the circle of cur vature at the point on the curve y = x2 where the tangent line…

A: To find and sketch the circle of curvature at a point on the curve y=x2 , where the tangent line has…

Q: 3. What is the equation of the tangent line to the curve x3 + x² = y which is parallel to the line…

A: Given the equation of the curve y=x3+x2 and the tangent line is parallel to 3y+x-5=0

Q: Set up the itegral that represents the length of the curve for 4=L x4 +L 4x2 for 12x< 2. Do Not…

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Q: The tangent of the curve x^2+y^2--7 * 2xy3DO at the point (1,1), is a. y-2-х. О b. y=x-2. O С.…

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Q: Suppose a curve is defined by the equati on y2 = x*(2- x). What is the equation of the line tangent…

A: Given curve

Q: Find to) - Isina the enclose by the Curve area and the line <x ハ

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Q: the tangent line to the graph (x^2 + 4)y = 8 at the point (2, 1).

A: Use formula of  equation of tangent  line

Q: If the normal to the curve y-f(x) at the point(3,4) makes an angle of Pi with the positive x-axis…

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Q: Find the exact length of the curve y3 = 22 from (-1,1) to (8, 4).

A: Use formula of length of curve

Q: Find the slope of the tangent line to the curve (a lemniscate) 2(z + v²) = 25(z² - y³) at the point…

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Q: Find the equation of the tangent line to the curve y = rVI at the point (4, 8). %3D

A: We have to find the equation of tangent

Q: Find the slope of the tangent line drawn to the graph of 2x2−xy−y3=5 at the point (2,1). Enter exact…

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Q: What is the length of the curve y3/2+4 from the point (1,5) to (4,12)?

A: To find: The length of the curve y3/2+4 from the point (1,5) to (4,12).

Q: 2. Find the equation of tangent and normal for the curve xsin2y = ycos2x at

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Q: 3 at the point 7, 3 is: The slope of the tangent line to the curve y %3D

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Q: Find the are length of the curve 2x = 3 y over the interval from y=0 to y=1

A: To find: The arc length of the curve in the interval . Formula used: The arc length of the curve…

Q: is the tangent line to y= 1/2arctan(1/5x) at the point (5,π/8)?

A: Answer and explanation is given below

Q: 9 Find the length of the segment 16 between the lines. y- 1-x + arcsinx of the curve -0, x

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Q: hat is the families of the curve of all circles with fixed radius r and tangent to the x-axis

A: Given           Radius of circles =r      and all circles are tangent to the x-axis.…

Q: 7. Find the slope of the line tangent to the curve at the point (2,1). x²y + xy² = 3x %3D

A: 7. The equation is given by x2y+xy2 = 3x                                                ......(1)…

Q: How many tangent lines to the curve y = x/(x + 1) pass through the point (1, 2)? At which points do…

A: The tangent lines to the curve y=xx+1 passes through the point (1, 2)

Q: 4. Find the tangent line to the curve y = In(x + x + 1) with slope 1. (2점)

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Q: Calculate the length of the curve defined by x =- Vy(y-3)on the interval 1 < y < 9.

A: x=13yy-3,   1≤y≤9 Differentiating with respect to y, we get…

Q: Find the point P on the line y=3x that is closest to the point (40,0). What is the least distance…

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Q: Find the exact length of the curve. 1 y = -x° 4 x² -- In(x), 1<x< 4 | 2

A: Given curve, y=14x2-12lnx   ;  1≤x≤4

Q: At what exact point on the curve y = 9 + 2ex 5x is the tangent line parallel to the line 5x – y = 4?…

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Q: What is the average distance between the parabola y = 7x(16-x) and the x-axis on the interval…

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Q: 2. What is the slope of the line tangent to the curve 8x3-y²=4 at the point (1,-2)? CAL normal line…

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Q: 9. Find the equation of tangent and normal for the curve xsin2y = ycos2x at A

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Q: 7. Find the slope of the tangent line at point (-2,2) on the curve flx) = 2x² + 3x. %3D

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Q: Kappa Curve: x²y² + y* = 2x² %3D

A: We are asked to find the slope of the tangent line at the given point

Q: Find an equation for the tangent line to the curve + xy - y = 1 at the point (2, 3). %3D

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Q: .3 The curve y3Dx+ x*-x has two horizontal tangents. Find the distance between these two horizontal…

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Q: 2. Find the curve that passes through the point (1, 3) and whose tangent line at (x, y) has slope

A: Solve for the curve

Q: Find the length of the arc of the curve 9y2 = 4x³ from the origin to the point (4, ). %3D

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Q: Find the length of curve along y = x² from (0,0) into (2,4).

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Q: 6. Find the equation of tangent and normal for the curve xsin2y = ycos2x at

A: Given that: x.sin2y=ycos2x