Find the relative maximum of the curve y = x5 – 3x3 + 20x – 2. A. 46 B.24 С. 32 D. 50

Q: Consider 2 2.4 3 f(x) 0.8 5.5 Find the curve fitting y(x)- Ax + B

A: Let's Solve,

Q: Find the point of inflection of the curve 6x – x' +5 y = 7 b. (2, 4) d. (3, 1) а. (0, 1) с. (2, 3)

A: Inflation point of a curve is a point on the curve at which concavity of the curve changes means it…

Q: Find the length of the curve below from the the point P = (1, 2) to the point Q = (8, 5). 2² = (y –…

A: The length of arc for curve y=fx from x=a to x=b is given as follows. L=∫ab1+dydx2dx The given curve…

Q: Find the shortest distance between and the curve y=\x-1. Select one: V11 a. O b. O c. V13 O d. 2

A: Let (x,y) be the point on the curve where the distance to the given point is shortest. So the…

Q: The length of the latus rectum of the curve x² – 12y = 0 is -12 -3 Option Option 2 12| 3.

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Q: Find the exact length of the curve given by 2t2 t3 (0 <t < 5). x = Length = ||

A: Solve for the length of curve

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: 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: A particle follows the trajectory x(t) = 3 + 2t, y(t) = 10t – t2 with t measured in seconds and…

A: Given: xt=13t3+2tyt=10t-t2

Q: Find the length of the curve. x = 4t, y =- 3/2,0st s9 0 st 122 3

A: Arc length of the given curve

Q: The x coordinate of the point of intersection between the two curves Y = e2lx and y = 1 is

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Q: For the curve given by x = vt and y =÷(t² – 4), t 2 0 find the slope and concavity at the point…

A: Given, x=t x4=t2 and y=14t2-4 we also write it as, y=14x4-4 Slope:-  y'⇒x3 at point (2,3)…

Q: Find the exact length of the curve. =글Vy (y-3), 16 <y< 25 X =

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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: Find the exact length of the curve. Vy (y - 3), 16 < y < 25 X =

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Q: Let the equation of curve c be x=2t, y=t3, t∈[0,2]. What is the value of the integral ∫c -y2dx +…

A: Explanation of the answer is as follows

Q: Find the length of the curve. y=1/6(x^2+4)^3/2, 0 less than or equal to x less than or equal to 2

A: Find dy/dx of the given function

Q: Find the length of the curve given by x(t) = 1 + 3t² ,y(t) = 4 + 2t³, 0 <t < 1.

A: xt=1+3t2yt=4+2t3 Differentiate the above equation w.r.t."t"…

Q: Find the exact length of the curve. y = (1 + x2)3/2, 0 < x < 2

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Q: Find the lengths of the curves x = y2/3, 1 ≤ y ≤ 8

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Q: a) Find the length of the curve y = 5x/T - 6, 1<r< 3.

A: Arc length of the curve along x-axis

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 exact length of the curve. y = 5 + 2x³/2, 0≤x≤ 1 2.268 X

A:

Q: Differentiate implicitly to find the slope of the curve at the given point. x2+y2 = 1; (4, 7) O 7…

A: The given equation is:x2+y2=1The point is 4, 7

Q: Find the exact length of the curve. X = Vу (у — 3), 16 <y S 25

A: First differentiate wrt y

Q: Find the exact length of the curve. 36y =(x+4). 5 5 x s 6, y 20

A: Given: 36y2=(x2-4)3,  5≤x≤6,  y≥0 Arc length of curve y=f(x) on [a, b] can be calculated by…

Q: Find the exact length of the curve x=y4/4 + 1/8y2 where 1 is less than or equal too y is less than…

A: Given that           x = y4/4  + 1/8y2 , 1&lt;= y &lt;= 2 Here we have to find the exact length of…

Q: Find the lengths of the curves x = (y3/12) + (1/y), 1 ≤ y ≤ 2

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Q: Find the exact length of the curve y=x3/3 + 1/4x, 1 less than or equal to X less than or equal to 2

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Q: Find the length of the curve x = y2 — 2y, 0 ≤ y ≤ 2.

A:

Q: Find the length of the curve x = (y3/33) + (11/4y) on 3≤y≤5.

A: Consider the given curve f(y) and find the derivative w.r.t y.

Q: Find the exact length of the curve. x= (y4/8)+(1/4y2), 1&lt; y &lt; 2

A: The given function is,

Q: 19. For what values of the constants a and b is (1, 3) a point of inflection of the curve y = ax³ +…

A: Consider the value of y and solve:

Q: Find the exact length of the curve.y = 1 + 4x3/2, 0 ≤ x ≤ 1

A: Given curve is

Q: Eliminate the parameter to find a Cartesian equation of the curve for −2 ≤ y ≤ 4. x = t2 − 3,…

A:

Q: Find the length of the curve x=e^t -t, y=e^(t/2), -8 less than or equal to t less than or equal to 3

A: The arclength for parametric curves is: L = ∫ab(dxdt)2+(dydt) Given  x=et-t, y =et2,      -8≤t≤3

Q: Q: Find the point on the curve 4x' +a'y = 4a', 4< a < & that is farthest from the point (0,-2).

A:

Q: Find the exact length of the curve. x = (2y + 1)3/2, 0<y<3

A: Differentiating with respect to y, we get

Q: Q4/ Find the length of the curve y () (x² + 2) from x 0 to x= 3.

A: The length of a curve f(x) on an interval [a,b] is: L=∫ab1+(f'(x))2dx Where f'(x) is the first…

Q: Find the equation of the lines tangent to the curve x2 + y2 = 4 and parallel to the y-axis ? O A. X…

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Q: (c) Find the length of the curve described by r = e30 for 0 < 0< 4.

A: Given, r=e3θ for 0≤θ≤4

Q: 5. What is the equation of the curve AB? X Depth B Specific Energy a) y + 2gy Q? у + Q b) у + 2gy Q?…

A: The curve AB represents  specific energy

Q: Find the exact length of the curve. y ‹ = ²(1 + x²j³/2₁ 3/2, 0≤x≤ 5

A: The objective of the question is determine the length of the given curve.

Q: (b) Show that the points of inflexion of the curve y = (x- a) (x – b) lie on the | line 3x +a =4b.

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Q: (h) Write the conditions for a curve y = f(x) to be concave upwards and downwards.

A:

Q: 11. Find the slopes of the curve y y?- r2 at the two points shown hcrc. 2 (V3 = y2 - x?

A: we have the curvey4=y2-x2

Q: Determine d^2 y/ dx2 for the curve: y = 8x^3/2 + e^2x .

A: Given,             y = 8x32 + e2xNow,         y = 8x32 + e2xDifferentiating on both…

Q: Find the lengths of the curves x = (y/4)2 - 2 ln (y/4), 4 ≤ y ≤12

A: Given equation of the curve - x = y42-2lny4           .....................(1)Given intervals = 4,…

Q: d the exact length of the curve. =√y (y - 3), (y - 3), 4 ≤ y ≤ 16

A: