Q. 2) Write short answers for the following: (Any FIVE Questions) 1. What is the maximum or minimum point for the curve y = x -4?

Q: Find the length of the given curve. 4/3 3y2/3 X = -27 - 32

A: The arc length formula is L=∫ab1+f 'y2dy. Here, 3y43-3·y2332' =-1+64y2316y13. Thus, the length of…

Q: Find the length of the curve y = xVa 0 <x < 1.

A:

Q: 4/2 % for 0 sxsl. Find the length of the curve y+1=- 3

A: The equation is y+1=423x3/2.   Differentiate with respect to x.…

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

A:

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: Refer to the figure above. In the upward-sloping portion of the curve that connects points A, B, and…

A: Answer:- Independent

Q: b) How far should we let 0 run to traverse the curves one time only?

A: To find how far θ needs to run in order to traverse the the the curve one time only, we need find…

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

A:

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

A:

Q: find the length of the remaining part of the y = x³/12 + 1/x curve between the x = l and x = 2 apfog…

A: We have to find the length of the remaining part of the curve y=x312+1x between x=1 and x=2

Q: 9. Find the point of intersection of the two curves, * y = 2r-1 y = x-2r O(-) none of these

A: To find out the point of intersection of curves.

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

A:

Q: Find the exact length of the curve. y = x3/2, osxs 6 3

A:

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: 2 =(x² - 1)³/²,1 ≤ x ≤ 3

A:

Q: Find the exact length of the curve. 2 3/2 y = = 12, 0<xs 1

A: Given ,y=23x32Aim: To find length of curve in [0,1]We know that…

Q: 2. Find the exact length of the curve. y = 3 ,1 < x< 2 15+51

A: Find the exact length

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

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Q: Find the exact length of the curve. X = 8. 1sys 2 4y2'

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Q: d the exact length of the curve. y = 1 + 8x3/2, Osxs1

A:

Q: For what values of c does the curve have maximum and minimum points? F(x) = 2x + cx +10x Select the…

A: For curve has both maximum and minimum  f'(x) = 0 has both real zeros/roots.

Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y = x – 3x? + 4x – 12…

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Q: 5 6. -9 -4 6. -4 -6 -1 a x + nb

A:

Q: Find the length of the curve. 30) x = 3 ty 3/2 - y 1/2 from x = 16 to x = 25

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Q: Find the length of the curve. x=(y - 1) 3/2 from y = 1 to y = 4 O 7 O 10 21 2 O 1

A:

Q: Find the exact length of the curve. y (y-3), 4sys 16 X =

A: use derivative for finding the exact length.

Q: y = 2x-3 2 x² + 4

A:

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

A: First differentiate wrt y

Q: 1. Find the length of the curve 4Y, 1<Y<2 8

A:

Q: Q1/ Find the equation of the circle tangent at least to three lines (y = 1, y 5, x 2 and x = 7). %3D

A: We have considered the first 3 lines as the line of the tangents For more see below

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 y=x3/3 + 1/4x, 1 less than or equal to X less than or equal to 2

A:

Q: y² = x x-1

A: We have to sketch the following curves.

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

A: The given function is,

Q: 1 Find the length of the curve y (x2 + 2)3/2 from x = 0 to x =9. 3

A:

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: 4 - Which of the following is the shortest distance from the point (5, 0) to the curve y = V2x ? 7…

A:

Q: Find the exact length of the curve. x = et - 4t, y = 8et/2, 0 sts 4

A: We find dx/dt and dy/dt

Q: 5. Find the length of the curve = = = (1 ²+2) X=- 3 9 0≤ y ≤ 4

A:

Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x

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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: For what values of a and b is (2, 2.5) is an inflection point of the curve x?y +ax +by = 0? What…

A:

Q: Find the exact length of the curve. x = 8 4y2' 1sys 2

A: Given, x=y48+14y2,1≤y≤2

Q: Explain how to find the length of the curve                         r(t) = ⟨ƒ(t), g(t), h(t)⟩, for a…

A: To Determine: Explain how to find the length of the curve Given: we have rt=&lt;f(t),g(t),h(t)&gt;…

Q: 7. Find the points of intersection of the following curves and draw the figure. x? – 3y = 0; x² + 2…

A: We have to solve these two equations to find intersection points of these two curves.

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: r= g° ,0<g<\5

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Q: 2 Determine the length of the curve = = t³, y: 31² 2,0 ≤t≤ √3.

A:

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

A: