10) Employ the following methods to find the maximum of the function from previous Equation. (a) Golden-section search (xi = -2, xu =1, ɛ: = 1%). (b)Parabolic interpolation (xo = -2, x1 =-1, x2 = 1, iterations = 4). Select new points sequentially as in the secant method. (c) Newton's method (xo = -1, ɛ: = 1%).

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A:

Q: 8. Find all points on the graph of y = (x + 3)² at which the tangent line is parallel to the line…

A: The given graph is y = (x +3)2 To find the points on the graph at which tangent is parallel to the…

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

A: Let a family of curves be given by the equation gx,y=Cwhere C ia a constant. for the given family of…

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A: Proceed as shown below...

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Q: Find the orthogonal trajectories for the family of curves 6x² + y² -9ax=0.

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Q: In the given equation , find the orthogonal trajectories for the family of curves. Use a graphing…

A: Solution:Given          y2=Cx3Formula:d(xn)=nxn-1∫xn dx=xn+1n+1+C

Q: Find the formula for a parabola with its vertex at (9,4) and with a second derivative of -3. f(x)=

A: let's equation of parabola is given by y=ax2+bx+c                                              ..1…

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A: Given          5x2-4y2=C       Differentiate w.r.t to x       10x-8y dydx=0…

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Q: 4) Find the orthogonal trajectories of the family of curves

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Q: 3. If y = 2 – 1, find the length of the graph of f from point z = 0 to a = 1.

A: Here, the given function is: y=f(x)=423x-1 To find the length of the curve from x=0 to x=1

Q: In the given equation , find the orthogonal trajectories for the family of curves. Use a graphing…

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Q: At what point on the curve y =[In (x +4)]2 is the tangenthorizontal?

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A:

Q: Find the error propagated from the function y = 3x* if an error of 0.06 occurs in the independent…

A:

Q: Find the error propagated from the function y = x³ if an error of 0.05 occurs in the independent…

A: For a function y=f(x) If  error in y is ∆y when error in calculating x is ∆x dydx=∆y∆x

Q: Find the orthogonal trajectories for the family of curves x2 − 2y2 = C . Use a graphing utility to…

A: Concept: Trigonometry is used in finding distance and angles, there are six trigonometric ratios…

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A:

Q: If tanh x = 12/13  find the values of the other hyperbolic functions at x

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Q: <, y) = )-« lustrate with a sketch. y 4 3 3 2 2 2 1 -4 -3 -2 1 1 2 4 -4 -3 -2 4 -4 -3 -2 /1 -1 -2 -3…

A: Topic:- calculus

Q: Find the orthogonal trajectories for the family of curves 3x2 − y2 = C. Use a graphing utility to…

A: Given:  The family of curves: 3x2 − y2 = C

Q: he line tangent to the graph of y=In(3x)+ 2x e at x =1 6

A: Equation of line is given as   y-y0 = dydxat x=1*(x-x0) Given,x0 = 1y = ln(3x) + e2x6y0 = ln(3x0)…

Q: Find all points on the graph of 3x 2 + 4 y 2 + 3xy = 24 where the tangent line is horizontal

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Q: 2. Find the family of orthogonal trajectories of the given family of curves in the following…

A:

Q: Find the point (xo,yo) on the graph of y = x' + 9x² + 7x – 5, at which the slope of the tangent line…

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Q: Find an equation of the line tangent to the graph of the function: f(x) = V2x² – 1 at point P(-1;1).

A: Given:- f(x) = (2x2-1)(1/3)  To find:- Equation of tangent line at point p(-1, 1) on given curve

Q: Find the orthogonal trajectories for the family of curves y2 = Cx3 . Use a graphing utility to graph…

A: Given curve is y2=Cx3.

Q: 4)Solve for the family of curves of straight lines with y-intercepts thrice as their corresponding…

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Q: In the given equation , find the orthogonal trajectories for the family of curves. Use a graphing…

A: Solution:Given     x2-2y2=CFormula:d(xn)=nxn-1∫xn dx=xn+1n+1+C

Q: Show that no point on the graph of x 2 - 3xy + y 2 = 1 has a horizontal tangent line.

A: Given  x 2 - 3xy + y 2 = 1

Q: At 6:00 am, ship A is 200 km west of port, heading east at 25 km/h. At the same time, ship B is…

A: Given:  At 6:00 am, ship A is 200 km west of Port, heading east at 25 km/hr.and at the same time,…

Q: 4. Find the orthogonal trajectories of the family of parabolas with vertices at the origin and foci…

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Q: of X メ curve Finu ん terms passes thrOush 11っの)

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Q: Find the error propagated from the function y = x³ if an error of 0.06 occurs in the independent…

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Q: Find the critical points of y= -2x^2 +4x +3 and apply the Second Derivative Test to find the maximum…

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Q: The slope of the tangent line to the parabola y = 3r2 + 6x + 2 at the point ( – 2, 2) is: The…

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Q: find equation of both the tangent lines to the elipse x^2+4y^2=36 that pass through the point(12,3)

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Q: Graph the Ine whose x-tercept is -I and whose y-intercnpt is 1.

A: Given,           The line whose x-intercept is -1 and y-intercept is 1.We know that,           The…

Q: The ________ of a sine or cosine curve represents half the distance between the maximum and…

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Q: 4. Jacobi is seated on the line tangent to the graph of  y =2x3 -3x2 -12x +21 at x =2.

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Q: 5. Find the point on the parabola y=-x+3x+4 where the slope of the tangent line is 5.

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Q: Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.) y = 19k

A: The objective of the question is find the orthogonal trajectories of the family of the curves.

Q: 2. Find an equation of a curve satisfying the ff. condition and passing through the point (0, -1).

A: dxy-dy1+x3=0A first order separable ODE has the form of Ny·y'=MxLet y be the dependent variable.…

Q: Sketch, by hand (without using any graphing device), several trajectories in the phase…

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Q: Find the maximum and the minimum points of each function on the given interval. 13. f(x) = 4x-3x2-6x…

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Q: 2 Consider the curve given by f(x)=x²³x + 5 find the equation to the tanget to the curve at point…

A: We know that a line which touches the curve fx at one and only one point is called a tangent line.…

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Q: Find the orthogonal trajectories to the family of curves: -1).

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Q: Find the family of orthogonal trajectories of the given family of curves in the following equation…

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