Find the clamped cubic spline that interpolates (0,0),(1,1),(2,2) and satisfies the condition: s’(0) = 1 and s’(2)  = 1.

Q: Find both first partial derivatives. z = 15XVY 15xVy %3D dz az

A: We need to find partial derivative.

Q: 2. Find the coordinate of the points on the cardioid r=1- cose at which there is a horizontal…

A: We are given the polar curve: r = 1- cosθ use formula:         x=r cosθy=r sinθ then,  dxdθ=-sinθ+2…

Q: Find the equation of the tangent plane to th surface 3x? + 5y? + 4z2 = 24 at the point (1, –1,2). 1.…

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Q: A point moves along the intersection of the elliptic paraboloid z = x² + 3y² and the plane y = 1. At…

A: Point moves along the intersection of the elliptic paraboloid z=x2+3y2 and the plane y = 1. We have…

Q: Which is the linear differantial equation into which the Bernolli differantial equation transforms

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Q: 5. Deduce the standard linear approximation of 1 x2+y2+z2 at Po(1,2,3).

A: The general formula of the standard linear approximation for f(x,y,z) is generally given by,…

Q: Find the orthogonal trajectories of the famil y of curves x'yxy=c where cis constant

A: Given:    x3y-xy3=c      Differentiating by using power rule we get…

Q: (6) Find the orthogonal trajectories of the 3C cos 0, where C family of curves r being parameter.

A: Answer

Q: Find the least squares quadratic which best fits the curve Y= ex interval •< X<I ao+aix +azx over…

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Q: Find the orthogonal trajectories of the given family of line y = Ce-mx with m held fixed. %3D

A: Given: y=Ce-mx

Q: Find the symmetric equations for the normal line LN to the surface S:f (x, y) = 5Vx2 + y? at the…

A: if  f is  function of (x,y,z) then gradient of f is defined asfx i + fy j + fz k ∇f is the normal to…

Q: Find the partial derivative at point(u,v)=(-4,0) of w=ln(xa+yb+za),x=uevsin u y=uevcos u, z=uev,…

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Q: The value of the line integral fydx + xydy over the straight-line path C from (0, 0) to (1, 2)…

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Q: Find an equation of the tangent plane to the surface 9x2 + y2 + 4z2 = 25, at the given point (0, −3,…

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: 4. Estimate the In (1.1) and sec (0.1) using a linear approximation and without using any kind of…

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Q: ih fcuv, w) and its partial derivatives v and w with respecttou and and are Continows that u-x-y, V=…

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Q: Consider a closed rectangular box with dimensions xx  ft by  yy  ft by zz ft. If xx  is increasing…

A: Proceed as shown

Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 &lt;=t&lt;= 2pai closest to the point (3/4,…

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Q: Find the particular soluti y' + 3x²y = 3x² %3D Initial Condition: y = 6 %3D

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Q: Find the orthogonal trajectories of the one parameter family of curves ex+e-y=c

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Q: The value of the line integral I- [Adl where A-(2x+y)£+(y-x)ý along the parabola y=x^2 and form…

A: Evaluate: I=∫A.dl              ...(1)WhereA=2x+yx∧+y-xy∧

Q: Find an equation for the tangent plane to z-x-y = 3 at the point (2, 1, 8) Z - ) %3D

A: given z-x2-y2=3 at point 2,1,8

Q: Find the equation of the plane tangent to the graph of z + xyz = 33 at (1,2,3).

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Q: Find the least squares quadratic & bj xj which best fits curve Y = sin(x)

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Q: Determine the equation of the normal line to the surface z2 cos(x + 2y) at the point (2, –1, 0).

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Q: The Normal line at the point (0, –1, 1) to the 3 surface exy - xy² + z³ = -2 is 7=y+1=² Select one:…

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Q: Find the orthogonal trajectories of the family of circles passing through the points (1, −2) and (1,…

A: Given that

Q: Evaluate the line integral Sc (2x² − 3y) dx + xy dy, where the curve/path C is the line 3 y = 2/2 x…

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Q: Find both first partial derivatives. Z = 13xVy az %3D az %3D ay

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Q: Distinguish briefly the Skewness and kurtosis

A: Skewness is a measure of symmetry where symmetry means equal proportion to the left and right to the…

Q: 5. Find the orthogonal trajectories for a family of circles tangent to the at y-axis.

A: Here we have to find the orthogonal trajectories for a family of a circle tangent to the x-axis and…

Q: Find the tangent plane to the equation z 2y cos(5x – 4y) at the point (4,5, 10)

A: Given; z=2ycos(5x-4y) at the point (4,5,10)

Q: What is the moment of inertia about the x-axis bounded by the curves y² = -16(x-4), the line 8x-15y…

A: here we have to find the moment of inertia about x axis so we can use integration to find this.

Q: Obtain the particular solution for: 2y" +2y=2sinx y(0)=0, y'(0) =1 By using method of variation…

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Q: For rigid-body motion, the strains will vanish. Under these conditions, integrate the strain…

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Q: 2. Show that cos(wt – B), coswt, sinwt are linearly dependent functions of t. Show Complete Solution

A: Given that: cos(wt-B), coswt, sinwt

Q: Find valume bounded by abave Z:4-20 and below by Z-xy 2.

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Q: Calculate the curve integral ∫c ( 3x2 - 3yz + 2xz )dx + ( 3y2 - 3xz +z2 )dy + ( 3z2 - 3xy + x2 +2yz…

A: Using green's theorem to find the line integral.

Q: Does the the paraboloid z = 1 – 2x² - - y² have a tangent plane at some – x + y + z = 1?

A: Introduction: Let P0=(x0,y0) is a point in the domain of f, and S is a surface defined by a…

Q: Find the families of characteristics of the PDE (1-x²)w„ - u,, = 0 in the elliptic and hyperbolic…

A: Pde

Q: Find the equations of the tanget plane and normal line to the graph of In(z2) x -= 3y³ – Vx at the…

A: Given graph is                                                        lnz2x-eyx=3y3-x Again…

Q: 5. Find the moment of inertia of a plate covering the first-quad rant region bounded by y2- x, x-:…

A: Plot the given conditions for finding the boundary limits.

Q: Find the orthogonal trajectories of the family of curves r 5C sin 0, where C being parameter.

A: Follow the below steps to find the orthogonal trajectories. Differentiate the function with respect…

Q: Find the linearization of ƒ(x) = 2x at x = 0. Then round its coefficients to two decimal places.

A: Given function is,

Q: 10. Find a tangent plane to z² – x² +y² = 1 at (7, –5, 5).

A: To find a tangent plane to the given curve at the point (7,-5,5)

Q: (6) Find the orthogonal trajectories of the family of curves r= 2C sin 0, where C being parameter.

A: See the detailed solution below.

Q: Determine the equation of the normal line to the surface z2 = cos(x + 2y) at the point (2, –1,0).

A: We have  z2 = cos(x+2y) ⇒cos(x+2y) - z2 = 0  So, F(x,y,z) = cos(x+2y) - z2  Thus,  ∇F(x,y,z) =…

Q: Find the first partial derivatives of 3x – 2y f(x, y) = at the point (x, y) = (1,4). 3x + 2y af…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Find the orthogonal trajectories of the families of Parabolas y a + 8az + 16a, which passes through…

A: