Q.No.1. (a) Let h(u, v) = In(n – u² + v) + VVv-u , Where n=540. Find its domain and sketch the Graph.

Q: Consider the following T-ARCH model: h = 8+a,e,+yde. (1, e, <0 (bad news) de e, 20 (good news) a) If…

A:

Q: 1. Find the orthogonal trajectories of the given family of curves: a. y= Ce¯mx; with m held fixed b.…

A: This question is related to family of curves, We will solve it using given information.

Q: 4. Determine the maximum point of the the graph of y = 12 sin(π – 2x), for x = [-T, T).

A: Given:         y=1-2sinπ-2x     To get the maximum value of the function the derivative is equal…

Q: Find the linearization L(x) of y = e In(x) at a = 1. L(x) = %3D

A: Given a function f(x)=y=e3x ln(x) To find the linearization L(x) at a=1 The linearization L(x) is…

Q: 4. Find the orthogonal trajectories of the family of curves y= Ce“ + 10

A: Here we have to find the orthogonal trajectories

Q: 3) A hot cup of tea has temperature T(1) = 198 °F, one minute after it has been sitting on the…

A: To calculate the local linearization of the temperature at t = 1.

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

A: Consider the given curve. r=2Ccosθ          (1) Find the derivative of the given equation.…

Q: (6)Find the orthogonal trajectories for the given families of curves 2x2 – 3y = K. Where K is a…

A: We have to find out the orthogonal families of given function Given function   2x2 -3y=K  ;    where…

Q: Write the general solution of the fourth-order DE y(4) – 2y" + y = 0 entirely in terms of hyperbolic…

A: We have to find the general solution of the differential equation y4-2y''+y=0. The auxiliary…

Q: 7. Evaluatexyddx+e*dy where C goes along the x-axis from (0,0) to (2,0) and then along the parabola…

A:

Q: 1. Any function y = f(x) can be expressed as x = f(y) in standard mathematical methods for solving…

A: Given: For any function y=f(x) can be expressed as x=f(y) in standardmathematical methods for…

Q: 6. Find a cubic function f(r) = ar³ + bx² + cx +d that has a local maximum value of 3 at r =-2 and a…

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Q: e. Find points on the graph of xy°z² = 16 that are closest to the origin.

A: Let P be point (x0,y0,z0) Then, distance between P and origin is given by

Q: 32 Q3: If f(z) Find the residues at all the poles of f(z) !! (Z+2)2(Z2-1)

A:

Q: Find the linearization L(x) of y = e5* In(x) at a = 1. L(x) =

A: Given that:y=e5xln(x)a=1To find the linearization

Q: Graph it excel     y = mx + b In T(s) In (Lm) 0.4472136 0.2 0.54772256 0.3   0.63245553…

A: Open excel,save the file Type the given data in tabular form Select Insert Tab, select insert line…

Q: 4. Find the orthogonal trajectories of the family of curves y=Ce*™ +10

A: We have to find the orthogonal trajectories of the family of curves

Q: 49.) Find the minimum distance from the point (2, 1, 4) to x + y + z = 4 by using the LaGrange…

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Q: Let C be the shortest path that connects a to ni and I = J. (coshz – 1)dz. Then I=-sinh T+ T(i-1)…

A:

Q: 4. Find the orthogonal trajectories of the family of curves y = Ce* +10

A: Given that : y = Ce2x + 10

Q: 4. Find the orthogonal trajectories of the family of parabola described by the equation (y– 3) = Cx.…

A: The solution of the problem is given in the next step.

Q: 1. Find the orthogonal trajectories of the given family of curves: Circles through the origin with…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 1. Consider the function f(x, y) = In(25 – x² – y²). %3D а. Find and sketch the domain for this…

A: Given function   f(x,y)=ln25-x2-y2

Q: The

A: Below is sketch of  the given function.    Rotation about x axis will give a volume in 3D plane.

Q: 2. Consider the following (knapsack) LP: = 150r1 + 100x2 + 99x3 51x + 50r2 + 50r3 S max z 100 T1,…

A: We find the solution of the given linear programming problem we first find the solution of the…

Q: 1. Find the orthogonal trajectories of the family of curve a+3y2 = cy ,where c is an arbitrary…

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Q: 5) Construct a linear approximation of the function f(x ) = lacX+s) about the point x,= 1. Compare…

A: Tangent line approximation or linear approximation is very significant in differential calculus.…

Q: |-4 Let y =||-3 and u =||-4 7 Compute the distance d from y to the line through u and the origin. d…

A: Solve for the distance

Q: nake/s the DE nonlinear y' =1-xy+ y2

A:

Q: (3) (a) Find the local linear approximation of f(x) = /1+x at xo = 0. Use your approxima- tion…

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Q: With y=c1.x2+k curves and curves x2+2.y2-y= c2 intersect perpendicularly. Where C1 and C2 are…

A: Given two curves are y=c1x2+k   and x2+2y2-y=c2  , where c1 &amp; c2 are arbitrary constants. Let us…

Q: SSS zdV Q3: Evaluate E + y² + z² = 1 and x² + y² + z² = 4 in the upper where E lies between the…

A: We have to evaluate the integral ∭EzdV, where E lies between the spheres x2+y2+z2=1 and x2+y2+z2=4…

Q: 8. DETAILS SCALCET9M 3.10.003. Find the linearization L(x) of the function at a. Rx) = Vx, a = 64…

A: given,

Q: 27. Find the length of the curve Vcos 2t dt y = from x = 0 to x = "/4.

A: The given curve is We know that by Second Fundamental theorem of calculus ,if F(x) is continuous on…

Q: let fie) - 71* Ihen f has a stotionary point at z- The stationary point is CNo arswer given Oa local…

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Q: 1. Find the orthogonal trajectories of the given family of curves: a. Circles through the origin…

A: As per the company rule, we are supposed to solve only one problem with a max of three subparts.…

Q: obtain a slope field and add to it graphs of the solution curves passing through the given points.…

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Q: 4. Find the orthogonal trajectories of the family of curves y= Ce“ +10

A: Given that, Family of curves is following, y = Ce2x + 10…

Q: {x} € 1, Show that property (3) of a matroid implies: For any S e there exists y € S, such that S \…

A: Following is the definition of a matroid. A finite matroid M is a pair (E,?), where E is a finite…

Q: 4) Find the orthogonal trajectories of the family of parabolas y – 3 = c(x + 1)².

A:

Q: 4. For the function f(x, y) = exp (ax + by) find the maximal possible value of the directional…

A: In this question we will use basic of calculus i.e concept of vector calculus. We will find the…

Q: Riemann sits on the line normal to the curve y=x2 -3x+2 at x = 1

A: Given           y=x²-3x+2 and x=1  Slope of the curve is given by =dy/dx

Q: 1. Find the optium path for f=xy³ from (2,1,2)

A:

Q: (6) Find the orthogonal trajectories of the family of curves r= 5C cos 8, where C being parameter.

A: we have to find the orthogonal trajectory for the given function

Q: 5) a) Compute Ko for the function f0=V+X by using the de finition of the deniratire, b) Find the…

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Q: 1. Find the orthogonal trajectories of the family of curves y³ = 3(x – c). Draw a few representative…

A: The orthogonal trajectories are the curves that are perpendicular to the family everywhere.

Q: A clamped cubic spline for a function f on 0,3 is given by [1+ax² -2x', S(x) = . [1-2(x-1)+b(x-1)² +…

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Q: Find the orthogonal trajectories of the family of curves ey + 2x2 = k.

A: Given,  ey+2x2=k

Q: Let C be the shortest path that connects a to zi and =J. (coshz - 1)dz. Then I=0 |=-sinh n+ n(1-i)…

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.