Q2 : (A) Find tan-1(-5+i) dz (B) find f. where c is the circle 12z + 2il = 4 z+4

Q: ) Write the equation r2+r(sin 0-6 cos 0) = 0 in Cartesian coordinates and identify the corresponding…

A: Solution is given below:

Q: The curves T1(t) = (2t, t“, – 4t) and T2(t) = (sin(5t), sin(t), t) intersect at the origin. Find the…

A: Given that  The curves R1 and R2  Intersect at origin  To Find the angle between the curve

Q: Find the lengthof the curve r = a sin² (0/2), 0 0

A:

Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <: sos

A: See the attachment

Q: Find the arclength of y = 2a/2 on 1 <a< 2

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Q: Find the arc length of the graph by partitioning the x-axis. y = x2/3 + 1, from x = 1 to x = 8

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Q: Find the length of the arc of the parabola  x^2 = 4y from x = -2  to x = 2.

A: I am attaching image so that you understand each and every step.

Q: Find the arclength of y = 4x³/2 on 1 < x < 3

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Q: Use the graph to approximate the number of points of intersection of the graphs of y1 and y2.

A: We are asked to find the solution of the graph

Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <- 4

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Q: jw F(w). [a - acos (wr)] - A 1 Tjw jwF(W) = -2A (1-cos (WT)). Tjw jwF(W) = -2A (asin ² (WT)) Tjw How…

A: since we have a trigonometric identity:                                   cos(2θ) =1-2 sin2(θ)⇒ 2…

Q: Give a rough sketch of the graph of the curve r= 1+ cos40, 0 < 0<2r.

A: The given curve is  r=1+cos 4θ,  0≤θ≤2π

Q: Find the arclength of y = 2a³/² on 1 < æ < 2

A: Answer is mentioned below

Q: Where do the curves of y cos(x) and y = x³ - 1 = intersect? Use bisection.

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Q: The curves r¡(t) = (2t, t², t³) and r2(t) = (sin(t), sin(3t), 2t) intersect at the origin. Find…

A: If there are two curves y=f1(x) and y=f2(x) which intersect each other at point (x0, y0).  The angle…

Q: For r=sin40, (i) sketch the curve. (ii) Find the area of one loop of the curve.

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Q: Q4\ Find an equation for the tangent line drawn to the circle (x- 3)2 + (y + 3)2 = 50 at the point P…

A: We Know that A tangent to a circle at point P with coordinates is a straight line that touches the…

Q: Find the arclength of y = 3r/2 on 1 < a < 3

A: As we know that the expression for the arclength is:   l=∫x1x21+dydx2dx...(1)   Given: y=3x32x→1 to…

Q: dz Find an upper bound for 9c z4 –5z²+6 dz, where c is the circle |z| = 4.

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Q: Sketch the graph defined by the parametric equations x = e' -t and y = 4e? for 0st<2. Indicate on…

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Q: Find the arc length of the graph y = V 2 49 - x

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Q: Evaluate |2*(x +7) – 2y ds C where C is the circle of radius 1 centered at (-3,0) and lying on the…

A: Since the integral ins on the plane x=-3 so the integral becomes:  ∫Cz3x+7-2yds=∫Cz3-3+7-2yds…

Q: Find the arc length of the graph by partitioning the x-axis. y=(1-x2/3)3/2 , from x= 1/64 to x=1

A: Given function is y = y= 1-x2/33/2 from x= 1/64 to x=1 The arc length of a curve on the interval [a,…

Q: = fx x²zdx- dx − yx² dy + 3 dz along the curve C shown in the figure. - Z 2 2 [x²zdx - yx² dy + 3 dz…

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Q: Find the arclength of y = 2x/2 on 1 < x < 3

A:

Q: Find the equation of the circle tangent to 3x+y+14=0 and x+3y+10=0 with radius square root of 10

A: A tangent to a circle is perpendicular to the radius vector on the point of contact. To find the…

Q: Q2 : (A) Find tan-'(-5+i) dz (B) find g. where c is the circle |2z + 2il = 4 z2+4

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: Q3: Find and classify all fixed points and plot the portrait on a circle for the system 0 = 2 + 2…

A: Given equation is θ.=2+2cosθ. We have to find and classify the fixed points of this system. Then…

Q: Find the arc length of the graph by partitioning the x-axis. y =2/3(x2 + 1)3/2, from x = 2 to x=7

A: The arc length of a curve y = f(x) over an interval [a, b] is given by the formula

Q: (y - eCos(e25! dx + (x2 + y+1) dy, where C is the circle r = 2.

A:

Q: The equation for the tanget to graph of y=sin^1(x/2) at the origin is

A: Given, y=sin1x2 Differentiate the given function with respect to x we get, dydx=cosx212 At point…

Q: Graph the curve: x = 3et cos(t),    y = 3et sin(t),    0 ≤ t ≤ π and then find the exact length of…

A: The provided parametric equation of the curve is as below

Q: xy = -4 and y² = 2х

A:

Q: Find the arc length of the graph y =(x2 + 8)°/2 from x = 1 to x = 4. 12

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Q: The curves r1(t) = (3t, t2, t) and r2(t) = (sin(t), sin(5t), 5t) intersect at the origin. Find their…

A:

Q: Evaluate |*(x + 7) – 2y ds where C is the circle of radius 1 centered at (-3,0) and lying on the…

A:

Q: Find the length of the curve r = 4 – 4 sin 0

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Q: Evaluate f. y3 dx - x3 dy where c is the circle x2 + y2 = 4

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Q: Find the lengthof the curve r= a sin² (0/2), 0 s0s T, a>0

A:

Q: find the arc length of the graph f(x) = x5/10 + 1/6x3  over [2,5]

A: Let y = f(x) be a function.Then, the arc length formula for the graph of the function over [a,b] is,

Q: Find the arclength of y 4x3/2 on 1 < x < 2

A: Here in this question given that y=4x3/2 and find the arc length. Between x=1 to x=2.

Q: Find the arclength of y = 2x/2 on 1< x < 3

A:

Q: Find the arclength of the curve y=3/2x^2/3 for x=1 to x=8.

A: Find the arclength of the curve y=3/2x^2/3 for x=1 to x=8.

Q: Consider the two graphs y= 2x and x2 - xy + 2y = 28. The absolute value of the tangent of the angle…

A:

Q: 2. Find the SA generated by rotating the first quadrant portion of the curve y = 9- x2 about the…

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Q: 3. Plot both the following curves on the same set of axes. r = 5 - 4 cos e and the parabola y = r.

A: Given

Q: 3. Draw the following curves on the grid provided y=-2 sin (x+30°) - 1 -90 90 180 270 360 -1 -2 -3

A: (x+30) represents a horizontal shift of30° to the left.(1 unit on the graph !!)-2 represents…

Q: 8. centered at Which of the following equations represents the circle with radius F 16x2 + 16y2- 16x…

A: