23. Find all points of inflection of the curve y=2r – 12r² + 10x+3. A) x=-1 and x= 1 B) x=-1 C) x=-1 and x=0 D) x= 1 E) x=1 and x=2

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: (b) Investigate where the curve y = xy4 - x² is concave up and concave down?

A: Given curve is y=x4-x2 find the concavity of the given curve

Q: 5. Trace the curve r = sinocos³o.

A: Given curve: r=12sinθ cos3θ

Q: 2 The length of the curve y = 312 between x = 0 and x = 1 is 3 %3D %3D

A: Answer is 4√2/3 unit.

Q: 9. Find the angles at which the curve y =x - x intersects the x-axis.

A: Given: The curve y=x3-x intersects the x-axis

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A:

Q: Evaluate (x+ y)ds where C is the straight-line segment x = t, y= (4- t), z=0 from (0,4,0) to…

A: Given that x=t,y=4-t,z=0 from (0,4,0) to (4,0,0) evaluate ∫cx+yds

Q: (5xy --- 6x(2^

A: Given,        F=(5xy-6x2)i+(2y-4x)j and   y=x3 from the point (1, 1) to (2, 8).

Q: 2. Prove that the following curves are intersecting with a right angle: 5y-2x+ y –x*y =0 2y+5x+x*…

A: Given curves are  5y-2x+y2-x2y=0and2y+5x+x4-x3y2=0

Q: 4. y = x2--Inx x = 1 ve x = e

A: Topic- application of derivatives to find angle between curves

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

A:

Q: Compute Sc(2x + V) ds, where C is the curve from (0,0) to (2, 4) along y

A: Given

Q: Now compute [(x − 3y² + 2) ds where C' is the union of the curves C1 and C2. C1 is the line segment…

A:

Q: 7. Find the length of the curve y = (* Vt3 -1 dt 1<t<4. 12.4

A:

Q: 4- Find the length of the curves in Exercises. 1. y = (1/3)(x² + 2)³/2 from x = 0 to x = 3 3. x =…

A: for a function of the form y=f(x) length of the curve from x=a to x=b is: L=∫ab(f'(x))2+1dx and for…

Q: Determine equation of tnagent line to the common curve of 2 surfaces w/ equations: z = x? + y – 2xy…

A: follow next step

Q: Find the length of the curve x = 5-t, for 1 < t < 2. length = y = 3-t, z = 3t 5,

A:

Q: Show that the curve y =(1 + x)/(1 + x2) has threepoints of inflection and they all lie on one…

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Q: Determine a, b, c and d so that the curve y = ax^3 + bx^2 + cx + d will have a critical point at the…

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Q: set up intergral for the length an of the Curve 3T y%3DZ0* sin cx), 04XE

A:

Q: Find the length of the part of the curve y = = between x = 1 and x = 2.

A:

Q: 4- Find the length of the curves in Exercises . 1. y = (1/3)(x² + 2)³/2 _from x = 0 to x = 3 3. x =…

A:

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

A: The formula is L = ∫ab 1 + dxdy2dy

Q: If lx + my = 1 touches the curve (ax)" + (by)" = 1, show that %3D )+) = 1.

A:

Q: 4. Find the exact length of the curve. 36y2=(x²-4)3,2≤x≤3.y≥1

A:

Q: Which of the following is the least distance from the point (2, –1,1) to the plane x + y – z = 2?

A: Given: The plane equation is x+y-z=2and the distance from the point is 2,-1,1 To find the least…

Q: Find the are length of the curve 2x = 3 y over the interval from y=0 to y=1

A: To find: The arc length of the curve in the interval . Formula used: The arc length of the curve…

Q: Prove that the following curves are intersecting with a right angle: 5y-2x+ y -x²y =0 2y+5x+ x* –…

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Q: Ex: Find egns of the line thru the pt ( -!,), perpendicular bo the line 3x= 2y == and paralled to…

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Q: Let C be the curve y = x³ – 3x2 + 4x – 1 joining the points (1, 1) and (2, 3). Find the value of…

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Q: Describe the traces of the curve x2 + 9z2 = 9 in the vertical planes (those parallel to the…

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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…

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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: 36y2 = (x2 − 4)3,    2 ≤ x ≤ 6,    y ≥ 0

A:

Q: Evaluate aned on c indicatid curve 2. 2. y+ Y( sm3x +ca 32,22 3t ,4=t,0zt2|

A:

Q: (b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is…

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Q: 3- Find the length of the curves in Exercises 1-4. X = (y3/2/3) - y¹/2 from y = 1 to y = 9

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Q: Find the length of the curve. y = (4 - x2/3) 3/2 from x = 1 to x = 8 O 9 O 12 O 18 O 6

A:

Q: 6.2 Finl the Voune of the Selid enclosed by the curves y=eX, y=0 x=0,'= "about the x-axs.

A: Given: y=ex, y=0, x=0, x=1 From the given curves the bounded region is as shown below; Apply the…

Q: Find the exact length of the curve. 1 y = -x° 4 x² -- In(x), 1<x< 4 | 2

A: Given curve, y=14x2-12lnx   ;  1≤x≤4

Q: (B) Find the length of the curve y 4 -Inx for 1<x <3

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Q: 4. Prove that the following curves are intersecting with a right angle: 5y-2x+y²-x²y = 0 2y +…

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Q: 6 - Find the length of the curve y = (x)7 from the x = 0 to x = 4. a) O 8/27(10^(3/2)+2) b) O…

A: .

Q: 1 y == (x² + 4)°%2 ,0 sxS 2 (x2 + 4)°/2 ,0<x< 2 6. deur die berekening van die volgende bej…

A: The given function y is - y = 16x2+432     ........(1)Formula for calcualting the lenght of a curve…

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

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Q: IFind the exact length of the curve x= 3t -t, y=3t² ,0<t<2 ||

A: We have to find the exact length of the curve. The length of the curve is given by

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Q: Identify the length of the curve 1X = ²+2y — In(y + 1), for 0 ≤ y ≤ 2. - 8

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Q: 4- Find the length of the curves in Exercises. 1. y = (1/3)(x² + 2)³/2 _from x= 0 to x = 3 3. x =…

A: