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Q: Calculate the integral xy² dy – x²y dx where L is along the curve x + y ² = a? (a > 0) in a…

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Q: Evaluate the following line integral along the curve C. (x- y)ds; C is the line segment r(t) = (t,…

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Q: Evaluate the iterated integral. T/4 r9 y cos(x) dy dx Jo

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Q: write an ntegral fer the sSurtare Ĥ rea o btaned bir otating about Y 2 the as graph of y=…

A: The given function is  Y= f(x) = 3+√x-1 ,1 <=x<=5  And y= 2    We have to draw the graph of…

Q: :+cos(x2) dz. =(s* + 1) 4.1 with C: |z- il -. 4.2

A: Explanation of the answer is as follows

Q: If z= t(x,y), where X = rCOse and y= rsine, %3D Show that 12 dz 12 dz dz dr dz del + dx

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Q: Find dey -. The initil dx² condition Xo=0i y=10, %%=5&h=,by using yro1), given Runge -Kutta method…

A: Given second order differential equation is d2ydx2=y3                  (1) with initial condition…

Q: Supply the missing integrand and limits of integration. J- Sor"y dyds = (a) [ L* 6z*y dzdy = dy /2…

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Q: Calculate the following integrals. In both cases the curve C has a counterclockwise direc- tion: 4.1…

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Q: Consider the curve r(t) = (t, 3 cos t, 3 sin t) for t > 0. COS So r(t)dt Compute the integral above.

A: ∫0πr(t)dt=∫0π<t,3cos t,3sin t>dt               =∫0πtdt i+∫0π3cos tdt j+∫0π3sintdt k…

Q: auchy - Goursát heorem to show that dz = 0 %3D 22 + 5z + 6 Cia tho girelo Lel hoth diroction

A: In this question, concept of Cauchy Goursat Theorem is applied. Cauchy Goursat Theorem If a function…

Q: Suppose that the radius r and surface area S = 4πr2 of a sphere are differentiable functions of t.…

A: Given surface area of a sphere, S=4πr2, where r is radius of sphere. It is given surface area is…

Q: dw by using Chain Rule. (Your answer should not include z ond y. dt = z+v? z = cost + sin t and y=…

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Q: dy Sølve +y = 0, under the conditions that y= 1, dy 0. when t = 0. dt %3D

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Q: Evaluate the following line integral along the curve C. |(x- y)ds; C is the line segment r(t) = (t,…

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Q: 3. Given f(x,y) = xy + y2 +1° ey Verify that fry = fyx %3D

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Q: du Q. Show that du and dy for u = In Vx2 + y? %3D dy and v = tan

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Q: 4x - 6xy? + 3y² = 228; dx = 3, x = -3, y = 4 %3D

A: Given  4x3-6xy2+3y2=228 ; dxdt= 3   at     x=-3    , y=4

Q: Evaluate the triple integral 1 V1-y V4-z? y? COS cos (z? + y? + z?) dzdzdy. V12 + y? + z2

A: Given triple integral is ∫-11∫01-yz∫04-x2-y2cosx2+y2+z2x2+y2+z2dzdxdy To evaluate the integral.

Q: Evaluate the double integral f S (ax cos(y) + by + 6) dx dy where R R: |æ|+ |y| < 3. Türkçesi: R:…

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Q: Let y = V5- z. Find the differential dy whenz= 2 and dr = 0.1 %3D Find the differential dy whenz= 2…

A: y=5-x

Q: Suppose C is the curve r(t) = (6t,t°), for 0sts2, and F = (3x,3y). Evaluate F•Tds using the…

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Q: Let oce) = Jñ e %3D dt, xe R X- is sloww that e li) show that the function y = o)e* satirfies the…

A: The function is σx=1π∫-xxe-t2dt. To show: ∫abe-t2dt=π2σb-σa. Proof: ∫-xxe-t2dt=σxπAs e-t2 is even,…

Q: Which of the following integrals represents the length of the parametric curve z = 1+e, y=ť, 3 <t<…

A: In order to know the length of the given parametric curve we will use the formula  where  -----

Q: Consider the following line integral | (ædx + ydy + (xz – y)dz) along a curve C given by r = t2²i+…

A: We will find out the required value.

Q: Evaluate the following line integral along the curve C. - y)ds; C is the line segment r(t) = (t, 3t…

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Q: Evaluate dW at t = dt for the function W = xy x = sin t, y = cos t, z = t². 4 49л2 972 9x2 4 49л

A: Given: W=xyz,x=sin⁡t,y=cos⁡t,z=t2 Substitute the value of x, y and z in w , we get W=sintcostt2…

Q: Given that C is the curve r(t) = (cos t, t), for /2 sts T, convert the line integral | ds to an…

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Q: a/ tangent s lope rasinczo) ) when e zT 9. 父 A dy do 2 517 dる 2. fhe D not of tne above

A: Given,  r=sin (2θ) Recall:  Slope, m=dydx

Q: Evaluate the double integral f S (ax cos(y) + by + 4) dx dy where R: |x|+ |y| < 7. R 392 O a+b+196 O…

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Q: Evaluate the triple integral 2xe" sin z dV, where Q is the rectangle defined by Q = [(x, y, z)| 0…

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Q: Evaluate the line integral x° + y) ds C Where C is given by r(t) = 3ti+t°j for 0<t<1

A: The region C is given by: r(t)=3t i + t3 j  ;       for  0≤t≤1

Q: The total surface area S of a right circularcylinder is related to the base radius r and height h by…

A: We have to find dSdt related to drdt and dhdt where neither r nor h is constant and total surface…

Q: DIfterenti are (뉴) de Ipx tan x -In DIfterentiate exy te Yy 1, tnd y"

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Suppos analyts s? show work. you

A: Given that f is analytic. And z≤1 And f(0)=0 And f(5)≤5 The formula for derivative is,…

Q: Find the approximate value for f(x, y) = sin(t10ry + In(y)) at %3D (Yukardaki f(x,y) fonksiyonunun…

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Q: Evaluate the line integral fe 3y dx + z? dy + (25 - x) dz over the quarter of the circle of radius 5…

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Q: it was e Int, X=tan't he dy cquals- eanals etcos t tInt cos"t tsint sint ए +ऐ1m+-coे + cotit tè…

A: A detailed solution is given below.

Q: Use Green's Theorem to evaluate Se xy dx + (1 – æy³) dy where C is shown below y (1,4) (-1,2) 2 1…

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Q: Evaluate the double integral f S (ax cos(y) + by + 6) dx dy where R: |¤|+ \y| < 2. R

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Q: valuate the line integral J xev% ds where C is the line segment from > (1, 1, 1). This yields:

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Q: The radius r and height h of a right circular cylinder arerelated to the cylinder’s volume V by the…

A: The volume of a right circular cylinder is V=πr2h. Consider that neither r not h is constant. Assume…

Q: d the val 5) y= 2cos 30 6) y= 4sin 20 cos 0 7) cot F 7) y= sin (0-45) 8) y = 2 + cos 0 9) y= 3sin…

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Q: (b) Estimate the following integral: (x². + 4y² + 9) dz dy, where D is the circular domain r + y 4.

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Q: Suppose C is the curve r(t)= (3t,3t), for 0 st s2, and F= (8x,5y). Evaluate F T ds using the…

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Q: Evaluate the double integral f S (ax cos(y) + by + 7) dæ dy where R : |æ|+|y| < 10. R Türkçesi: R:…

A: We have to find the double integral.

Q: Find the exuct Sulutivn for y'=x+2Y

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Q: Compute the integral 10x/1+ 4y?ds over the curve C: R(t) = (t + 5, t), 0<t< 1.

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Q: the ( gmplicit valne ) Find differenciation of az at the given poin t. Sin (y)+ sin(yn) + Sin (z+X)…

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Q: By differentiation show that ∫ f(s)ds    +   ∫g(v)dv     =  0  (to to t)        (yo to y) becomes…

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.