Find the length (in units) of the curve y =    16 − x2between x = 0 and x = 2.

Q: Find the abscissa on the curve x²=2y which is nearest to a point (4, 1). А. 0 С.2 В. 1 D. 3

A: Use the distance formula then minimise using derivative.

Q: Find the points on the curve x2 + xy + y2 = 16 which are nearest and farthest from the origin.

A: Given curve is g: x2+xy+y2=16 If x,y is any point on the curve g: x2+xy+y2=16 Then square of the…

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

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Q: Find the length of the curve 4t2 -1 dt, y = %3D 1<x<3 8. 15 104 3 3.

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Q: The x coordinate of the point of intersection between the two curves Y e14a and y = 1 is = x =

A: Given: y=e14xy=1

Q: Explain the steps required to find the length of a curve x = between y = c and y = d. g(y)

A: Given the curve x=g(y). We need to explain the steps required to find the length of a curve between…

Q: The x coordinate of the point of intersection between the two curves y = el4a and y = 1 is

A: Equate both equation

Q: Find the exact length of the curve. y - 4 + 2x 3/2, o sxS1 1.547

A: Note: We are authorized to answer one question at a time, since you have not mentioned which…

Q: Eliminate the parameter to express the curve in the form y = ƒ(x) . x = 4t2, y = t3 - 1

A: We have given curves; y = ƒ(x) . x = 4t2, y = t3 - 1

Q: Express the curve by an equation in x and y given x(t) = e' and y(t) = 7 – e2'. a) O-x2 + y = 7, x 2…

A: simplify the equation and choose correct equation.

Q: Find the exact length of the curve.   y2 = 4(x + 4)3 , 0 ≤ x≤ 2 , y&gt; 0

A: Given: y2=4x+43,0≤x≤2,y&gt;0 To Find: Find the Exact length of the curve. Concept: Length of the…

Q: For the curve y=ax^3+bx^2+12x-7, what values of a and b will make the tangents to the curve at x=2…

A: Solution is here

Q: 1) Given the curve 2x? + y3 = x3 + y? find the x-intercept of the tangent line at the point (2,1)

A: We find dy/dx using the implicit differentiation and we plug x=2 and y=1

Q: Find the equation of the curve, if at any point on the curve y "= 1- vĩ and it has a tange line at…

A:

Q: For the curve y=ax^3+bx^2+12x-7, what values of a and b will make the tangent to the curve at x=2…

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Q: e length of the curve y = V 4 – x2, 0 <x< 2. ing the shape of the curve.

A: Use the arc length formula to find the length of the curve.  y=(4-x2)1/2 , 0&lt;=x&lt;=2

Q: Find the exact length of the curve for the parametric equation

A: Let's say the length of the curve is L.  0 ≤ t ≤ 1 Hence, the desired length will be calculated as:

Q: a)Find the exact length L of the curve 3y = (4x – 3), 1 0. Answer: b) Evaluate xe*dx Answer: .3 c)…

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Q: Find the exact length of the curve. y2 = 16(x + 3)3,   0 ≤ x ≤ 3,  y &gt; 0

A: Given: Find the exact length of the curve.

Q: Explain the steps required to find the length of a curve x = g1y2 between y = c and y = d.

A: It is given that x=gx for c≤y≤d.

Q: Find the point on the curve y = Vx closest to the point (1,0).

A:

Q: y = e*, 0<z<1.

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Q: C3. Find the length of the of the curve x= 1 from y = 1 to y = 2 %3D 4 8y?

A:

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: The slope of the curve y = (5x² + 8x + e)eje at x = 0 is

A:

Q: Find the exact length of the curve. y = 4 =Dx2-을 In(x), 1sxs6 =

A:

Q: For the curve y= e^-3x cos 2x, determine y'' + 6y' when x = 0.

A: In this question we will use basic of calculus concept of differentiation. We will simply…

Q: Find the exact length of the curve. y2 = 16(x + 4)3, osxs 2, y > 0

A: Given data:   The given expression is y2=16(x+4)3. The given limits of x is [a,b]=[0,2].   The given…

Q: Find the length of the curve r= e2θ, 0≤θ≤2

A:

Q: Find C so that the line y = 4x + 3 is tangent to the curve y x2 + C.

A: The given equations are y=4x+3 y=x2+c.

Q: Find c so that the line y = 4x + 3 is tangent to the curve y= x^2 + c?

A:

Q: 3 Find the length of the curve y = x² – 2 from x = 0 to x = 4.

A: Given curve is y=x32-2 Upon differentiating we get dydx=32x12 We know that length of…

Q: Find the angle between the curve 2y=e-x/2 and y-axis

A: we will see in next step

Q: The length of the curve y = (2+ 2x )3/2 between x=0 and x=2 is O 41/3 O 45/2 O 43/2 O 47/3 49/6 ООО…

A:

Q: of the curve yln x + 5x² + y' =13 at the point (1,2) dx b) Find

A:

Q: Find the length of the curve y = 4 1 between x 1 to x 2. %3D &x2

A: It is length of curve.

Q: Find the exact length of the curve. y2 = 16(x + 5)3,   0 ≤ x ≤ 1,  y &gt; 0

A:

Q: Find the angle between the curve 2y = e – x/2 and y – axis

A: Given the curve 2y =e^(-x/2) and y-axis We have find angle between curve and y-axis

Q: Find the exact length of the curve (a) x = 1+ 3t2, y = 4+ 2t³, 0<t<1 (b) x = e' cost, y = e' sin t,…

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

Q: 4.For the 2 curves xy = 8 and x2 = 64y, find the angle between the two tangent lines at the !! %3D…

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

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Q: n of the curve, L. (x+ 1)* , 0 0

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Q: Find the exact length of the curve. 1 + 8. X = 1 s y < 3 4y2'

A:

Q: Find the length of the curve 3y = (x² + 1) ? from x = 0 to x = 3.

A: Given:

Q: The x coordinate of the point of intersection between the two curves 12x y = = el2# and y = 1 is x =

A: Our Aim is to find the x coordinate of the points of intersectionbetween the two curves y=e12x and…

Q: Find the length of the curve y = x^4 for 0&lt;_x &lt;_1

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Q: What is the length of the -3< x S3 segment of the y = v36 – x2 www vwwb w e curve?

A: