2.2 Find upper bound of z + 4 -dz (z – 3i)3 + 1 where C is the circle |z – 3i| = 4.

Q: 2.2 Prove that Te -dz < 3 ez z2 +7+1 where C is the arc of the circle |2| = 3 from z = 3i to z = -3.

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Q: (1) Evaluate the line integral 4xy dx + (2x² – 3xy)dy if the curve C consists of the line segment…

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Q: (a) Compute the arc (1,3, 1/3). F(t) = (t, 3, t) between the points (0,3, 0) and length of the curve

A: These 2 are unrelated problems as anyone can be solve without any help of another. So by Bartleby…

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

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Q: 1. Find the area of the region enclosed by loop of the curve T = cos(46 one 1.0 y

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Q: 2. Consider any five points P1, Ps in the interior of a square S of side length 1. Show that one can…

A: To solve this problem we use the Pigeonhole principle . Pigeonhole principle : If there are m holes…

Q: Find the length of the arc of the given parabola: x²=4y from x=-2 to x=2

A: We know that the length of the arc of the parabola y=f(x) from x=a to x=b is given by L = ∫ab1+dydx2…

Q: 13.9. Let be the arc of the circle 2 = 2 from z = 2 to z = 2i that lies in the first quadrant.…

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Q: 1. Prove that the composite trapezoidal rule with h = 2-i, i E N, is exact for ſ cos? (Tx) dr

A: We know that in composite trapezoidal rule, we approximate the integral as follows: ∫abf(x) dx ≈  h…

Q: Find the exact length of the curve. v= In(1 – x²). y 0 <x < 1 In(|3|) - 8.

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Which of the following expressions gives the length of the curve defined by R(t) = tij +In tk…

A: We have to find arc length expression for the given vector function. Given is the curve…

Q: 2. KS is tangent to the circle at T. Secant KR contains P, the center of the circle. PR and PT are…

A: Firstly draw a circle with center P Now draw a tangent KS at point T

Q: Show that 22 dz = 0 1 – cos(2) whenever y is a closed simple smooth curve contained in a very small…

A: Solution: Here the integral is ∮+γz21-cosz We know that    cos0=1cos2π=1cos3π=1... Only z=0 is in…

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

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Q: Find the exact length of the curve. y = In(1-x), 0sxs 8.

A: Given that: y=ln 1-x2, 0≤x≤18

Q: 2.2 Prove that e? dz] < 3 +++1 where C is the arc of the circle |2| = 3 from z = 3i to z = -3.

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Q: 8., (x + y) dA, where R is the region that lies to the left of the y-axis between the circles x? +…

A: As you have asked to answer question 8, we will answer question 8.Question 8.The given integral…

Q: 7. (~Ch16 Review #6) Compute y3 dx + x² dy where C is the arc of the parabola x = 1- y² from (0, –…

A: In this question we need to find the given line integral .

Q: 24. Which of the following formulas would give the length of the outer loop for the curve: (Hint:…

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Q: (1) Find a point P in the first quadrant on the curve f(x) = such that the rectangle with sides on…

A: In the question we have to find the perimeter of the rectangle.

Q: 13.2. Find the length of the arch of the cycloid given by z(t) = a(t – sin t) + a i(1 – cos t), 0 <t…

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Q: Forz =x+jy determine the equation of the loci in the Argand diagram of: arg- %3D 4

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Q: 3 4. Find the arc length of the graph of the function f(x) =;(x² + 1)ī over the interval [0, 1]. =…

A: y =f(x) =23(x2+1)32f(x)=23(x2+1)32f'(x)=23*32(x2+1)12(2x)f'(x)=(2x)(x2+1)12 The Formula for arc…

Q: 21. ds: C is the quarter-circle r(t) = (2 cos t, 2 sin t), for 0SIST/2.

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Q: 2z-1 Find the upper bound of where C is the right half of the z* +5z +4 circle |z|= R, R>2

A: Given, I=∮c2z2-1z4+5z2+4dz, z=R, R&gt;2 Now, fz=2z2-1z4+5z2+4 For singularities of fz, we have,…

Q: In the case when U = x on the edge y = a (where Yo is a constant), a calculate C, inorder to show…

A: Given at y=a, U=ψ0ax     …Equation(1). And, on substitution of y=a in expression…

Q: QUESTION 3 Evaluate fds, where f(x,y) 2x +3y and C is the counterclockwise curve around the circle…

A: Given function is, fx,y=2x+3y The equation of circle is, x2+y2=4

Q: Question 3 z+7i+1 Find the upper bound of the integral- dz where C is the circle z-2+3 = 4.…

A: Given integral is ∫Cz+7i+1(z+3i-2)2+2dz where C is the circle z-2+3i=4 Here radius is 4. To find the…

Q: 9. Find the area of the surface generated when the given arc is revolved about the x-axis: 4x² +…

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Q: 2.2 Prove that e zp- 3 where C is the arc of the circle |2| = 3 from z = 3i to z = -3.

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Q: 9/ Find the Vale of the integrel ) Losz+Retz)r Imtz)} dz 3 is the Straitht line Segment from Zero to…

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Q: - Using Euler's equation, show that- : z fain (K 0)} - z sin Ø z2 – 2zCos Ø +1

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Q: 2.2 Prove that e zp- 3 2+z+1 where C is the arc of the circle |=| = 3 from z = 3i to z = -3. %3!

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Q: 1 Find the area of the surface generated by revolving the curve x = cos (3t), y 3+sin (3t) on 0sts…

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Q: Prove that e dz < ++1 3 where C is the arc of the circle |2| = 3 from z = 3i to z = -3.

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Q: 3. Discuss how to evaluate f () dz , where C is a simple closed curve C=10 enclosing the origin.

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Q: Part (a) Evaluate 100e dz, where C is the polygonal path consisting of the line segments from z =…

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Q: 7. Suppose that x2 + y? = r² and x = r cos 0, as in polar coordi- nates. Find дr ax дr and дх

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Q: Find the area of the specified region. Shared by the circles r=D 3 cos 0 and r= 3 sin 0

A: Consider the given circles r=3·cosθ and  r=3·sinθ To find the area of the region first find the…

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

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Q: #5. Evaluate the line integral (xydx +2x dy), where C is the arc of the parabola with equation y=…

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Q: Find the length of the curve. r(t) = (3t, 3 cos(t), 3 sin(t)), -3 sts 3

A: For the curve r(t) = f(t) , g(t), h(t)On the interval [a, b]The length is given by L =…

Q: Consider the region in the fourth quadrant between the circles x² + y² = 4 and x² + y² = 25 and…

A: answer is in next step. please give a like !!

Q: Evaluate | 9+x* dx+xy*dy along the positively oriented curve C where the C is the boundary of the…

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Q: Find the length of the curve defined by y = 3 In 3 from x = 8 to x = 9.

A: Use derivative of function and length of curve formula .

Q: 3) Find the exact length of the curve y = x² – In x for 1< x < 2. 1„2

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Q: 7. Let F = (2r sin(y)e", x² cos(y)e", a² sin(y)e*). %3D Find along the path c:7 = (sin(t), t,…

A: Given F→=2xsinyez,x2cosyez,x2sinyez. Find ∫CF→·dr→ along the path c:r→=sint,t,cost,-π2≤t≤π2. From…

Q: Express the circle specified by x = 2 cos(0) y =1+2 sin(0) in Cartesian coordinates and find the…

A: Solution

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

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