find the orthogonal trajectories of the family ofcurves. Sketch several members of each family. kx2 + y2 = 1

Q: Find all the local maxima, local minima, and saddle points of thefunction9. ƒ(x, y) = x3 - y3 - 2xy…

A: Consider the provided function, fx,y=x3-y3-2xy+6 Find all the local maxima, local minima, and saddle…

Q: Find the max. and min. values of (x, y) = x² – xy + y on the quarter circle x² +y =1 where x.y20.

A: I use langrange multiplier method

Q: Find the exact length of the curve. y = 3 + 6x³/2, 0≤x≤1

A: Given :y=3+6x3/20≤x≤1

Q: Find the exact length of the curve.

A:

Q: b) How far should we let 0 run to traverse the curves one time only?

A: To find how far θ needs to run in order to traverse the the the curve one time only, we need find…

Q: Find the length of the curve: 7= Scos 4. t2.

A:

Q: utwards from the point (0 nd S, the top half of the

A: Given, the vector field                        E(x, y, z)=x, y, z-3this vector field can be…

Q: Find the family of oblique trajectories that intersect the family of the paraboles y = Cx at angle e…

A:

Q: Find an equation of the normal line to the parabola y = x – 9x + 5 that is parallel to the line x -…

A:

Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 8x – 6y on the circle…

A:

Q: B) Use Lagrange multipliers to find the the points on the circle a² + y? = ry has its extreme…

A:

Q: Find the orthogonal trajectories of the family of curves r² + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: Find the exact length of the curve. y = 5 + 2x³/2, 0< x < 1

A: Given: y=fx=5+2x32, 0≤x≤1 we know that lengthL of curve in interval a,b is given by L=∫ab1+f'x2dx…

Q: / Fit a curve of the form y = ax + bx² to the data

A: Given,    x 1 2 3 4 5 y 1.8 5.1 8.9 14.1 19.8 To find             y=ax+bx2…

Q: Use a formula to express y as a function of t if y = 6x + 4x and x = t- 1.

A:

Q: Find the points on the curve 5x + 5y? - 6xy - 6xy = 4 nearest to the origin.

A:

Q: y = -x³/2,0 < x< 1 3.

A:

Q: Find the exact length of the curve. y = In(1-x), 0sxs 8.

A: Given that: y=ln 1-x2, 0≤x≤18

Q: Find the length of the curve. y = 2 – 4x, 1<a< 3 O 54 3V17 O 17 O 2y17

A:

Q: Find the exact length of the curve.y = 4 + 2x3/2, 0 ≤ x ≤ 1

A: Please see the white board for the formua to calculate the length, L of the curve y = f(x), over the…

Q: find the orthogonal trajectories of the family ofcurves. Sketch several members of each family. y =…

A: Consider the provided curve, y=cx2 Find the orthogonal trajectories of the family ofcurves. First…

Q: find the point p such that v=pq has the components (5,-7,-4)

A: find the point p such that v=pq has the components (5,-7,-4)

Q: Find the linearization for f(r) 10, and use it to approximate 12 near a=

A: We want to find the approximate value of 112 by linear approximation of the function ,fx=1x by…

Q: Find the exact length of the curve.   y = 1+ 6x3/2 , 0 ≤ x ≤ 1

A: Find the exact length of the curve.

Q: Use the table, along with dimensional analysis, t

A: Given,              2078 in3

Q: x = t³, y = t²,0 <t < v3

A:

Q: Find the exact length of the curve. y = 2/3x3⁄2,    0 ≤ x ≤ 1

A:

Q: Determine the point(s) (if any) at whi

A:

Q: Find the length of the curve given by S(x) = (a -) defined on the interval (1, 2].

A: Consider the given curve:

Q: A molecule is moving along the x-axis such that at any time t 2 0 (in seconds), its position from…

A:

Q: Find the length of the curve r= e2θ, 0≤θ≤2

A:

Q: Solve The family of curves is given by the equation y = Inx". The orthogonal trajectories for these…

A: Steps to find the orthogonal trajectories of the  given family of curves : Find the differential…

Q: Find the exact length of the curve. y = In(1 - x²), o s x s

A: Solve the problem using definite integral

Q: determine the equation of the orthogonal trajectories of the following fsmilies curves: Circles…

A:

Q: Show the complete solutions, kindly include all the necessary drawings, graphs and illustrations.…

A:

Q: Find the exact length of the curve.y = 1 + 4x3/2, 0 ≤ x ≤ 1

A: Given curve is

Q: Find the orthogonal trajectories of the family of curves x² + Y? = R? %3D

A:

Q: Find the exact length of the curve. y = 3 + 8x3/2, 0<x<1

A:

Q: Find an equation of the normal line to the parabola y = x2 - 8x + 9 that is parallel to the line x -…

A:

Q: / Find the length of the curve y = (÷) (x²

A: Given,         y=13x2+232

Q: Let Q = 4x? + 6xy+ 4y². The points on the curve Q = 7 which are closest to the origin are:

A:

Q: Find the isogonal trajectories to a family of straight lines y= cx that cut the lines of the given…

A:

Q: Find the length of the curve r

A:

Q: Find the orthogonal trajectories of the given family of curves y? = tcx 1-cx

A: The orthogonal trajectory is the family of curves that is perpendicular to the given curve. The…

Q: to find the answer, using 9) Find the Linearization of (x) = a - integers

A:

Q: Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle e…

A: The answer is given below:

Q: Find the exact length of the curve. V=5+8x3/2 0<x<1

A:

Q: y = In(1 – a²) ; 0 < æs

A: Solution:-

Q: Find the points on the curve x2y = 2 nearest the origin.

A: The curve is x2y=2 Let x1,y1 and x2,y2 be two points, distance betwwen these points is x2-x12+y2-y12

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.