Q4 Which of the following gives the length of the graph of TT y = In(sinx) from x =- to x 3 3 a) 3 1 + cotx dx b 13 csc?xdx c) 3 V1 + csc?x dx d 13 cscx dx TT 3 El3

Q: Use the Theorem of Pythagoras to find the length of the line segment y = 3xfrom (1,3) to (2,6), and…

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Q: H.W: Use the Trapezoidal Rule with n=6 to approximate. Here f(x}=sin2x,a=0,b=x.

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Q: Given the double intergral 3 S.³ To √²+y² Evaluate the above dy dx intergral using cartesian…

A: some of the formula of integration . ∫1x2+a2dx=ln|x+x2+a2|+C∫xndx=xn+1n+1+C

Q: S (x, y) = sen (r² – 0²) + In(r® + 0), con Vr? + y? A r = = arctan

A: Given that, f(x, y)=sen2r2-θ2+lnrθ+θfor r=x2+y2and θ=arctanyx

Q: dz The possible value for , where is any circle not passing through z = a, traversed z-a once in the…

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Q: Question ): The integral that represents the length of the curve y = tan(2a), where <a <, is the…

A: Given y=tan2x

Q: Apply the method of Implıcit Di fferentiation to find dy in eq (i) angle O=45 with and loPI-r=472…

A: Given, x2+y22=16x2y.....1x=rcosθy=rsinθr=16cos2θsinθ Now diffrentiating the given function with…

Q: Q. Find the length of the arc of f(x) = ÷(x² + 1), 1< x < 4

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Q: at is the Ar+B drif A=0 and B 12+1 25 arctan (r2 +1) +c 25 0- Arctan x +c 25 o In |z² + 1| + C 25 25

A: Put value of A and B and then solve

Q: Q6. Let w = f(r,0), r = √x' + y³, 0 = tan'(y/x), ), find aw ?х > and ди ду in terms of r and 0.

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Q: Q4) The standard formula for the tangent of the sum of two angles is tan x + tan y tan(x +y) 1- tan…

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Q: Q3 Point out the singularity and is ty pe of follo wing fune tions 22 () d) Sin t2 24

A: Singularity

Q: The length of the curve y= In(cosx) between X=0 and X = TT/3 is given by: a. None of the other…

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Q: Ex: 1) Let f(x, y) = sin(xy) X to wake fa cont. function on all of R²? ,x = 0. How should you define…

A: The given function is fx,y=sinxyx, x≠0 and f(x,y) is continuous on ℝ2. To find: f(0,y).

Q: Compule he an Curvc given aM byO x= and ye 3tcos(t) 'from DLtL engh ot M pacbmeter 3t Sin (t)

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Q: ind the length of the curve x cos(t) + In(tan(;t)), y = sin(t), /4<t< 3n/4. %3D ength =

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Q: - If x=sect and y = tan t, evaluate at t of the following: 4. dy (a) dx d y (b) dx?

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Q: Given that 3x - tan y = 4, what is dy in terms of y? A 3sin y

A: I have provided solution in step2

Q: given sin -In\x+ y + 19| Ax, y) = V18 – (x + 11)² – (y + 10)² sketch domain p(-11+ v7, - 10) is…

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Q: The arc length of y = 5++ from x = 1 to x : 2x (A) f 1+ (5 ++² dx +2 dx 2x (B) 2x2 (C) f1+ x2 dx 2x2…

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Q: Solve the equation for x, where x is restricted to the given interval. y = 4 cot , for x in (0, 2x)…

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Q: 2. for, (x+y)X = tan-14x + TT* + dx dy a)- Find InIny

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Q: 2. It Z = e tanly) , wnere x = S"+ t and y=St, find 22 when S=1 and t =0 2t

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Q: Determine the so luti'on of the equertion: dy dx2y cot x= 1- 2xcot 2x- 2csc 2x

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Q: The approximation of I = , tanx dx using composite Simpson's rule with n=5 is: None of the choices…

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Q: Find the largest interval on which the following IVP has a unique solution. (2t+1)y"+ sin t +ey tan…

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Q: The approximation of I = f, tanx dx using composite Simpson's rule with n=5 is: O 0.6236 ) 0.6158 O…

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Q: EX: Show that o dz =2TL whcre CIS a unit Circle. Sal: Z= re. io dz = ire do ig ir e de %3D = 2i Note…

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Q: Which of the following is equivalent to / Isin(Inx?)]²dx , sin(Inx 14) dx A sin2(Inx 14) dx O (sin…

A: Given that, The given integration is following, I=∫[sin(lnx7)]2dxx We have to find the equivalent of…

Q: The approximation of I = , tanx dx using composite Simpson's rule with n=5 is: 0.6158 0.6165 None of…

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Q: dx Evaluate LJv by using Trapezoidal rule (up to three 1 + x? decimal places). [Ch-4(B), Expl-2]

A: We have to evaluate ∫01 dx1+x2 by using Trapezoidal rule.

Q: that y?=x+ sin Cxy) - T 2 and let ß Be the value of dy evalwated atlxy

A: Given- y2=x2+sinxy-π24 To Find- The value of dydx at π2,1 and considering that value as β and then…

Q: The approximation of I = , tanx dx using composite Simpson's rule with n-5 is: None of the choices O…

A: f(x) = tanx Each interval h=(b-a)/n =1-0/5=1/5 =0.2 xO=0, x1 =1/5, x2=2/5, x3=3/5,x4=4/5, x5=1…

Q: The approximation of I = f, tanx dx using composite Simpson's rule with n=5 is: None of the choices…

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Q: Use the trapezoidal rule with n = 20 subintervals to evaluate I L sin? (VRx) dx. %3D Note: R = 33

A: Solution:- We have to evaluate the integral I=∫15sin2Rxdx   where R=33 by trapezoidal rule with…

Q: find dw/ar if w = (x + y + z)?, y = cos(r + s), at the point (r, s)3(1,-1) x = r - s, z = sin(r + s)

A: Given w=(x+y+z)2 x=r-s y=cos(r+s) z=sin(r+s) point (r, s)=(1, -1)   when we differentiate partially…

Q: ()- 3. n = 2 In for 4 7y712 4 x = f (y) ; It Arc length %3D

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Q: Is it true that Arg(z) = arctan for x + 0, where x = Re(z) and y = Im (z) ?

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Q: Selve the boundaly value preblem (D+ 36)g = and y'(o) = 2 that yte=I Sin 6x, given %3D

A: We know, 1D2+a2sin ax = x2∫sin ax dx

Q: 2, If fCx)=xInCx²+), find the ea uation for t4e tan9ent 1ine to fCx) at x= 3.Hint: Remember the…

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Q: dr Let A be the area of a circle with radius r. If dt dA when dt 4, find %3D r = 3.

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Q: 4) Given: AB is an external tangent to Q0 and 0Q at points A and B, radi for O0 nd OQ are and 12,…

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Q: The approximation of I = S, tanx dx using composite Simpson's rule with n=5 is: O 0.6158 O 0.6236…

A: First option is correct

Q: Which one is the arc-length of the curve y =2/7x + 11, x E [7, 11]? 147x+280 dx 7x+ 11 14x2 +…

A: The curve y=27x+11 , x∈7,11

Q: (5) Under what Conditions is (ax+by) dx + (KX+LY)dy=o exact? selve the eXact equation,Ca, b,k, L…

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Q: The integral that represents the length of the curve 7(t) = (t, cos (2t312), sin (2t312)), where Ost…

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Q: Use the secant mèthod to calculate V5 correct to three decimal points. fix)= heration No. S(x.)…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 6. If x= sect and y=tant, evaluate at t =- of the following: dy (a) dx d'y (b) dx?

A: x = sect y = tant

Q: x sect and y= tant, evaluate at t = - of the follow 4 dy (b) d y dx?

A:

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.