Use prt1 of the fundamental thearemof calceles to fni the 'derivalive of the fune lion.

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Q: Find the points on the cardioid r = 1−cosθ at which there is a horizontal tangent line, a vertical…

A: Consider the given: r=1−cosθWrite the cartesian…

Q: State the theorem of Arc Length.

A: State the theorem of Arc Length.   The arc length is x360°2πR. here R is the radius of the arc and x…

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Q: Find the Contour integration to

A: ∫-π-π11+sin2xdx∫aafxdx=0, a≠∞=0

Q: From Rogawski ET 2e section 8.1, exercise 9. Calculate the arc length of y = - x - In x over the…

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Q: 1 Evaluate f - dz over the unit circle in counter-clockwise direction using the parametriza- tions

A: To evaluate, ∮1zdz over the unit circle counter-clockwise

Q: Find the orthogonal compliment to S span{ 0 }. ||

A: To find the orthogonal complement to S spanned by two vectors .

Q: Construct the bisector of XY.

A: According to our guidelines we can answer only first question . Kindly re-post other questions . (1)…

Q: Give two different parametrizations of the line through (4, 1) withslope 2.

A: Solution:GivenA point(4,1) with slope 2Formula:Equation of the line at (x1,y1)y-y1=m(x-x1)

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Q: what is the avorago valus OF a Funckon F on an Posterval [a,b]? 13 the given by vallis of Fa)-tan X,…

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Q: Compute paramenc curve Ogiven by bu Iine of the X= eEsinct) 二e ato t=

A: To Determine: Compute the tangent line of the parametric curve given by  Given: We have   x=etsint…

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A: rsin2x=cosxLet us change into cartesian coordinates uvPut u=rcosx and v=rsinxr×v2r2=urv2=uThis is…

Q: he segment AB by a scale factor of using point C as a center of dilation. Cons figure on the…

A: Please refer to the image below

Q: 1)cotx will be cont 0) is

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Q: 2? satis fies Verity that the functrun..u=l the threemdimensnal.aplae 5. e

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A: Consider two regions C1 and C2 then these can be defined as follows, Thus, C=C1UC2 The conjugate…

Q: function holomorphic in 2 except p in an open neighborhood of w, the

A: To prove, ∫Tf(z)dz=0

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A: Given: dydx=8sin(x) To find: Slope field of given equation.

Q: From Rogawski ET 2e section 8.1, exercise 7. 3 Calculate the arc length of y = x 7 over the interva…

A: use arc length formula for finding it.

Q: USE THE METHOD OF VARIATIOH Of PARAME TERS To SOLUE THE FOLLOWIHG DIFFEREHTIAL EQUA TION!…

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Q: Use either a computer algebra system or a table ofintegrals to find the exact length of the arc of…

A: Given curve is x=ln1-y2

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A: Integration of hyperbolic function ∫sinh(x) dx=cosh(x)+C Now, in the given problem to determine…

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A: Using the Residue theorem these types of questions can be solved by integration around the unit…

Q: 4) limo Arcstnxx to

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A: Check whether the given integral is and divergence or convergence

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A: The acceleration (a) of the particle is 0.25 m/s2. The body accelerates from rest until a time of 4…

Q: (4) Find the -periockic points and detorimme their sta. stakliny of hu)=EX %3D

A: 4) Given: h(x)=1-x3x+1 Determine the periodic point by substituting h(x)=x.…

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Q: Let C be the shortest path that connects n to ni and I = S. (sinhz + 1)dz. Then

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Q: perio dic funchion with pz Consider eren calaulate fCI.75)

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Q: Prove that L" (coshat sinat + sinhat cosat) %3D s*+4a*. 2a

A: The function F(s) is Factorize the denominator

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A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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Q: Evaluate: |2 esin dx, for n=8 using (a) Trapezoidal method, (b) Simpsons Method

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Q: )2. Find the paramehic from the cune check whether the cure is a repulor cuwe. AGo reparametije the…

A: Note: According to our guideline we will answer the first question as the exact one is not…

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A: Given,

Q: Use either a computer algebra system or a table ofintegrals to find the exact length of the arc of…

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A: The tidal resonance occurs when the tide excites one of the resonant modes of the ocean. The effect…

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A: Given: ft=t coshat   As we know from the property of the Laplace transform. Ltnft=-1ndndsnLft   And…

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A: The De Moivre’s formula or De Moivre’s Theorem states as: cosx+isinxn=cosnx+isinnxwhere i is the…

Q: "ind the orthogonal compliment to S = span{

A: Here we have to find the,

Q: Use a linear approximation to estimate V29. Show the work. Do not round your

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Q: What are the new coordinates of the point (18, 8) under the dilation (x, y) → (1.5x, 1.5y)? O (32,…

A: Given the co-ordinates (x,y)=(18,8)