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Q: Suppose that the error for the composite trapezoidal rule is given by h2 f" (µ), µ E (a, b).…

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Q: known as the loop of Descortes lea ond tor EECO,00) O(t)= ( 3+2 %3D Calculate the oreo of the region…

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Q: A natural cubic spline S on (0,2] is defined by Jsin - 1+2-r. S) = if Osr<l. |S,0) = 2+ b - 1) + cư…

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Q: Evaluate the line integral [6. 6ayⓇ ds, where C is the right half of the circle x² + y² = 4.

A: To evaluate :   ∫C6xy6ds, where C is the right half of the circle x2+y2=4 Prerequisite : We can…

Q: The speciat sotution to the equatio %3D ho A/y)=+X B/yo)=y - %3D d/other than that

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Q: 2) usins Culcuulus for parametrre curres. Show trat the aren of a idis e of radius Ris siren by…

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Q: The area of the surface formed by revolving the graph of x = /ỹ on [2,9] about the x-axis is given…

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Q: If R is the region boundeb by the square a|+|y = 1 then ffR(y-2)dA is equal

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Q: The numerical value of 34 3dA (where D is the region bounded by lines y=0 and x = 1, D and the…

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Q: 4. Which would not be sufficient to prove AWXZ AWYX? C ZWXZ = LY WZ А WX XW YW WZ D WX WX XY XZ WX…

A: To show that the given two triangles are similar we need to show that the sides of the two triangles…

Q: 5. Find the volume of liquid needed to fill a sphere of radius R to height h (Figure 18). R h…

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Q: find thearea of the. region.. R bounded. b. the. graphns. Of. the gienequations. y x-1j y=0, X= 2…

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Q: The area bounded by the curve y3a and the lines z 4 and a-9 above the z-azis is aquare units O 27v0…

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Q: 3. Find the area of the band cut from the paraboloid x² + y² -z = 0 by the planes z = 2 and z = 6.…

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Q: The area of a cylinder sector with radius r and central angle of radian measure 0 is A = r20, and…

A: If the area of the sector is 1 sq. unit, then A=112r2θ=1θ=2r2          ...(1)

Q: Consider the region enclosed by the curves y = a2 +1 and y = 2r + 1:

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Q: The path integral v- dr, where v = (sin y, x - cos y) and C is the perimeter of the triangle formed…

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Q: Let CR be the circle of radius R centered at the origin. Use Green's Theorem to find the value of R…

A: ∮ y3 dx+x dyUsing green's   theorem∮P dx+Q dy=∫R∫∂Q∂x-∂P∂y  dAP=y3                  Q=x∂P∂y=3y2…

Q: Find the anea of the vegion in quadrant Ps bou nodod ist 4 the conie the by the right by the line…

A: Given curves, y=ex+12,y=e-x+12,x=2 ln2 To find the area of region bounded by these curves.

Q: Find the sccond derivate Of the finctron Y =2*. Inx

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Q: A trapezoid has bases with lengths x + 3 and 3x — 1 and a median oflength 1 1 . Find the value of x.

A: Consider the given trapezoid: where, AB=x+3 and CD=3x−1,Median, XY=11From Formula,XY=AB+CD2

Q: Solve u +u =0 for the square mesh with boundary values as shown in Figure 11.14. Iterate till the…

A: Consider the given differential equation, uxx+uyy=0 Here we have to find the mess values which are…

Q: @ Consider the task of approximating 3x2 using the Compoute trapezoidal rule. How large should n and…

A: The error term in the composite trapezoidal rule is  h212b-af''ξ , where h=b-an Given f(x)=e-3x2…

Q: egral dS over the su 9, where n is th surface element

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Q: If the region R is bounded between two circles 961 x² + y? = 4, x² + y? then we have: 2л 3 sin(Vx2 +…

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Q: On cogely the r y Mesiduer to Cualiete Calular (os node

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

Q: 3) consider the regionnin the second quadrant betueer the circles x?+yZ=4andx2+y2=25, and above the…

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Q: 3. Evaluate ff Vr² + y²dA, where R is the region bounded by the circles with center R (0,0) and…

A: Given integral is: ∫∫Rx2+y2dA Where R is the region bounded by the circles with center 0,0 and…

Q: Find the exact value of arc length of the semicubical parabola y2 = x³ between the points (1,1) and…

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Q: The area bounded by the curve y = In(z) and the lines z = 1 and =2 above the z -azis is %3D square…

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Q: If the region R is bounded between two circles x² + y = 4, x² + y = 9, then we have: sin(Vx2 + y?)…

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Q: normed spore) is contimous Segpeue HEX. d:x--X(when x is a nome -> i.e

A: Given that X is a normed space The given function is continuous. Now take a sequence xn. Assume that…

Q: 9-The uolome of Abe colar height y is hy VE xy. Soppose that the uolome a right cir cular cone af…

A: Given a right circular cone with radius x and height y. Then volume of the right circular cone…

Q: Jraen fusk hon conespaaday to o d'u z ul) = flx). dx² Find the the egualido for conespoodiang to…

A: Given differential equation is d2udx2+u(x)=f(x)                   (1) boundary conditions are…

Q: Find the region bounderd ABOUE ly ther pauabola X= (y-2 and bounded kčlana by anothen panaivic Iy…

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Q: The largest interval for which the IVP : y' + Tm- = y(3) = 10 %3D %3D nigua rolution ir

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 3. Evaluate the integral *zp- where C is the circle |2| = 2.

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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: A string of length 1m attached with two points. The deflection in the string is given by y" + Ay =…

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Q: 7.38. Calculate the second moment of area for a 2 × 6 piece of lumber about the x-x and y-y axes, as…

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Q: Given: ARST = AXYZ; SK bisects ZRST; K YL bisects 2XYZ. Prove: SK = YL S

A: Prove SK≅YL.

Q: 3. Given the closed curve defined by y = vx in the first quarter up to 1000 = x (area production),…

A: FIND: a) how many unit squares it contains b) number of squares needed in the cover

Q: The numerical value of л за 3dA (where D is the region bounded by lines y=0 and x = 1, D and the…

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Q: (4) In the figure, Y is compact, BEX*Y. Show that T,(B)s TB) clesed X (T, is the nýuchikn funebran)…

A: Given that Y is compact and B⊂closedX×Y. The objective is to show that, π1B⊂closedX Let's define,…

Q: 8. Use Green's Theorem to evaluate px*dx+xydy where C is the triangle with vertices (0,0), (1,0),…

A: As we know from the Green's theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydA And The expression for the equation of…

Q: 3, Let R be the of: y: sinx region endlosed bu the grophs n enclosed by and 1 x70 . Groph R and…

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Q: i Apply Green's theorem to eve luate S [rex=y)dx +Cx+g)dy], where C is the bocundaug qxis aiad the…

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Q: 3 dz where C, is the top half of circle with radius (b) Compute the upper bound of 2,

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.