Q3/ Find the lengths of the curves (L) for the equation as shown below. (25 M.) x = (/3) + 1/(4y) from y = 1 to y = 3

Q: Find the equation of the tangent line to the curve y = x² – 5 if the tangent lir is parallel to the…

A: we know that if two lines are parallel then their slopes are equalGiven that the tangent line is…

Q: Q5: Does any tangent to the curve y vx cross the x-axis at x--1 If so, find an equation for the line…

A: It is required to find if any tangent to the curve y=x cross the x-axis at x=-1. First find the…

Q: Find the length of the curve x = 49 sec* t – 1 dt with 3 - - 6. Length is

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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 length of curve: y=3x^(3/2) from x=0 to x=4

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Q: Find the slope of the tangent to the curve at the point specified. x² +y² = 9 at (0, 3) The slope is

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Q: 4. Find the point on the curve y = 2x² – 12x + 5 where the tangent is horizontal.

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Q: Find the slope of the tangent to the curve a + 2xy+ y = 49 at (1, 6). The slope is (Enter undef if…

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Q: find the slope of the line tangent to the curve x2=y2+3/2xy at (4,2)

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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 length of the curve y x² Inx 8 at (2 <x< 4)? -

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Q: Find the point(s) on the graph y = x3 where the line through the point (4, 0) is tangent to y.

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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: Find the ponits on the curve 9y2 =x3 where normal to the curve makes equal intercepts with axes

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Q: Find the equations of the tangents to the curve x = 9t2 + 9, y = 6t3 + 6 that pass through the point…

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Q: Find the length of the curve parameterized by x = 2 + 3t² and y = 3 + 2t³ from t=0 tot = 3.

A: A detailed solution is given below

Q: At what point(s) on the curve x = (x, y) = 6t² + 4, y = t³ - 7 does the tangent line have slope?

A: This question is related to parametric curves and slope of tangent, we will solve it using given…

Q: find equation for the lines that are tangent andnormal to the curve at the given point. ex + y2 = 2,…

A: Given: Equation of curve ex+y2=2 and the point 0,1, To find: Equation of tangent and normal line to…

Q: Find the slope of the tangent line to the curve - 42? – zy + y - 4 at the point (– 2, 2).

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Q: Find the length of the arc of the curve 4y2 = 9x3 from the origin to the point (2,3v2).

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Q: Find equations for the lines that are tangent and normal to the curve at the point (1,1).. x³ + y² =…

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Q: Find an equation of the line tangent to the curve defined by æ° + 2xy + y% = 104 at the point (2,…

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Q: What point on the curve y = Vx is closest to the point (5, 0)?

A: Use distance formula between two point and then differentiate

Q: Q3/ Line A with equation y = -8x – 18 is tangent to the curve with the equation y = 4x + 2x? Find…

A: Given : The equation of the tangent line is y = -8x-18. The given curve is y = 4x+2x2

Q: Find the equation of the line tangent to the curve 3t2 + 8,y = 8t + 3 at t = 2

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Q: Find the exact length of the curve. 1 y = 1 + cosh(8x), 0 ≤ x ≤ 1 8

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Q: At which points on the curve y = 1 + 60x3 - 2x5 does the tangent line have the largest slope? 1 5…

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Q: Find the equation of the tangent line to the curve y=4+e2sinx at the point (0,5).

A: our objective is to find the tangent line equation.

Q: 8. Find the slope of the tangent of the curve x² + y² = 10 at the point (1, -3).

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Q: Find the ponits on the curve 9y2=x3 where normal to the curve makes equal intercepts with axes

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Q: 4. Find the equation of the curve for which y""= 2x³. The slope of the inflectional tangent at (-1,…

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Q: For the curve y = ax+ bx + 12x- 7. what values of a and b will make the tangents to the curve at x…

A: Given, The curve  y=ax3+bx2+12x-7 We have to find the value of a  and b such that tangent to the…

Q: The equation of the tangent line to the curve +y =64, at (6,-12) is 12 y=D (-6)+12 6. 6. 12 -6) – 12…

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Q: For the curve y = ax³ + bx² + 12x - 7, what values of a and b will make the tangents to the curve at…

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Q: Determine the point on the curve y 16 a² where the tangent line is horizontal. A (2, 12) (-2, -12)…

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Q: 2. Find the coordinates of the points on the curve y = r' - x² – x +1 where the tangent line is…

A: Solution:- step-by-step solution of above  question is given below.. The given curve is  y=x3-x2-x+1…

Q: Find an equation of the line tangent to the curve defined by æ° + 2xy + y = 104 at the point (2, 2).…

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Q: Find the slope of the tangent to the curve x^4+5xy+y^2=7 at (1,1). The slope is:

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Q: At what point on the curve x = (x, y) 6t² + 5, y = t³ - 2 does the tangent line have slope 11/22

A: This question is based on finding slope of parametric curve.

Q: At what points on the given curve x = 2t3, y = 4 + 8t - 11t2 does the tangent line have slope 1?…

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Q: 5. Find the equation of the tangent line to the curve y = x2 - 3x at the place where the parabola…

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Q: Find the length of the curve for 12x = 4y³ + 3y-¹ where 1 ≤ y ≤ 3 Enter your answer in exact form.…

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Q: 6. Find the point of inflection of the following curve. Express your answer as (a,b) Ex. (1,2) * y =…

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Q: At what point on the curve x = 9t2 + 6, y = t3 − 9 does the tangent line have slope 1/2?

A: Given parameteric equations of curve,   .x = 9t2 + 6 , y = t3 – 9   To find the point on curve…

Q: What is the slope of the line tangent to the curve y = 3x² + 6x +3 at x = 4? Oy' = 51 O y' = 30 O y'…

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Q: Q3/ Line A with equation y = -8x – 18 is tangent to the curve with the equation y = 4x + 2x². Find…

A: Given that the line y=-8x-18 is tangent to the curve with equation y=4x+2x2. Note that the slope of…

Q: Q2: Find the points on the curve y 2x3 -3x2 -12x + 20 where the tangent is a. perpendicular to the…

A: y=2x3-3x2-12x+20

Q: 4) Find the equation of tangent I point line to the circle below at point (1,-3). * x² + y² – 2x –…

A: Consider the given equation of the circle, x2+y2-2x-4y-20=0 The equation of the tangent line passing…

Q: Find an equation of the line tangent to the curve y = v4x – 3 – 1 and perpendicular to the line x +…

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Q: At what point on the curve x = 3t2 + 1, y = t3 – 5 does the tangent line have slope ? 2

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