66) The curve y = ax2. point (2, 28) and is tangent to the line y 2x at the origin. Find a, b, and c. + bx c passes through the

Q: Determine a, b, c and d so that the curve y = ax³ + bx² + cx+d₂ pass through (-1, -1) and have at…

A: To Determine: Value of a, b, c and d so that curve y = a x3 + b x2 + cx + d

Q: 19. Does the line that is tangent to the curve y = x3 at the point (1, 1) intersect the curve at any…

A:

Q: 5. Trace the curve r = sinocos³o.

A: Given curve: r=12sinθ cos3θ

Q: Find the condition that the line ax+by=1 may be normal to the curve an-1y=xn

A:

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 following curve. y = 2x + 4 on 3-2, 24 (Use calculus.)

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Q: 1. Find the are length of the curve x (+ 2)/2 from y=0 to y-1

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Q: Find the length of the curve defined by 2? = 2y3 from x = 0 to x = 4:|| %3|

A:

Q: Determine the coefficients a, b, c, d that will make the curve y = ax3 + bx2 + cx +d passes through…

A: Given y=ax3+bx2+cx+d

Q: 12. The line y = 8x + b is tangent to the curve y = 2x². Determine the point of tangency and the…

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Q: The curve y = a x 2 + b x + c passes through the point ( 1 , 2 ) . The line y = 2 x + 1 is tangent…

A: Given that the curve passes through a point.

Q: Find the distance from the point Q to the line ℓ.

A: Given: Q=0, 1, 0, l with equation xyz=111+t-203.

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 the condition that the line ax+by =1 may be normal to the curve an-1y =xn

A: Given thatan-1y =xn Solution is as follows

Q: b) Find the point on the curve y Vr that is closest to the point (7,0).

A: Find the point to the curve y=(x)^(1/2) that is closest to the point (7,0)

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

A: we have to solve the problem

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: Find the length of the curve. 29) y = 1,3. 6. 1. from x = 1 to x = 3 2х

A:

Q: For what values of a and b is the line-3x + y-b tangent to the curve y = az3 when x-5? a=

A: The value of slope of tangent to the curve at the point is the value of its derivative at that…

Q: A line is tangent to y = x - 2 at (2,6). What is the coefficient of x when the line is in the form…

A: Given curve y=x3-2    ;   (2,6)

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

A: Use formula of length of curve

Q: y = 4 1 ,2 In x, 1<x < 2 2 -

A:

Q: Find the length of the curve y=x^3/2 from the point (1,1) to the point (4,8).

A:

Q: 3 at the point 6, 2 The slope of the tangent line to the curve y |3| is: The equation of this…

A: Derivative y with respect to x and then substitute the given point to find the slope.

Q: Prove that there no line through the point (0,1) is tangent to the graph of y = x*.

A:

Q: 20. Does the line that is normal to the curve y = x² + 2x - 3 at the point (1, 0) intersect the…

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Q: 8.) Find the exact length of the curve y= over the interval (0.4]. 2 %3D -

A: Given,          The exact length of the curve y=x22 over the interval 0,4 .

Q: The line that is normal to the curve x2 + xy - 2y? = 0 at (3,3) intersects the curve at what other…

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Q: The slope of the tangent line to the curve y at the point ( 5, is: The equation of this tangent line…

A: Given curve is : y=3x To find the slope of tangent at the point 5,35 and equation of tangent in the…

Q: Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Since we have to find value of a,b,c and d

Q: Find the are length of the curve x = (y² + 2)/2 from y-0 to y=1

A: First, calculate dxdy for the equation, x=13(y2+2)32  . Then, use the formula, L=∫ab1+dxdy2 dy to…

Q: Show that the tangents to the curve y2 = 4px from any point on the line x = -p are perpendicular.

A: The given curve is,

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: The tangent line to the curve y = 1/3x^3−3x^2+9x+12 is parallel to the line 8x−2y=3 at two…

A: given: the tangent line to the curve y=13x3-3x2+9x+12 is parallel to the line 8x-2y=3 at two points…

Q: 4 Find a. the equations of the tangents to the circle x +y + 4x – 2y – 24 = 0 at the points where…

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Q: A curve like Y = is called a serpentine. 1+2x2 3 n equation of the tangent line to this curve at the…

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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 length of the curve 9y2=8x3 from x=o to x=12 when y>0

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Q: The slope of the curve 2y = ax + b at (1,-1)is -1.Find a, b.

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Q: 2 Show that the line y = x +3x+m for all values of m. y= mx+4 will touch or intersect the curve

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Q: At what point is the tangent line to the curve y³ : = 6x² perpendicular to the line 2x + y = 2 = 0?…

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Q: What are the coordinates of the points in the graph of y-x+6x – 13=0 in which the tangent line is…

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Q: Find the exact length of the curve. 36y² = (x²-4)³, 4≤x≤6, y 20

A:

Q: 5. Find the length of the curve x = +22 from y =0 to y=3.

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Q: 12)What is the slope at (1,2) for curve define by xy^2=4?

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Q: I need to solve this question

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Q: Find the exact length of the curve. y = 9 + ¹ cosh (8x), 0≤x≤7

A: The curve y=9+18cosh8x, 0≤x≤7

Q: Find the exact length of the curve. 36y² = (x²-4)³, 5≤x≤9, y 20

A: