Find the isogonal trajectories to a family of straight lines y= cx that cut the lines of the given family at an angle a, the tangent of which equals k.

Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + BỊ.

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Q: Find a function f (x, y) that has the line y = 3x - 4 as a level curve.

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A: topic - equation of tangent line

Q: Suppose a person wants to travel D miles at a constant speed of (30 + x) mi/hr, where x could be…

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Q: The tangent line to the graph of y = In(2x) is perpendicular to z + 4y = 1 at the point where Select…

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

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Q: Find the linear approximation to the equation xy f(x, y) 2. at the point (4,6,4), and use it to…

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

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Q: 1. Answer the following questions: (a) Find the linear approximation of y- f(x)-Vr at a 256 and (b)…

A: Firstly, we will calculate f'(x), then f(a), f'(a).

Q: The linear approximation at x and where B is:

A: Given a trigonometric functionf(x)=sin(6x)

Q: b) Find the orthogonal traJec tories of the families o f r=5acose where la) parameter

A: We have to find the orthogonal trajectories of the families of r=5acosθ where a is parameter.

Q: Find the linear approximation to the equation f(x, y) = 2, at the point (4,2,4), and use it to 2 %3D…

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Q: Show that if P lies on the intersection of the two curves x2 − y2 = c and xy = d (c, d constants),…

A: Solution:Givenx2-y2=c     and   xy=dTo prove tangent curve at P are…

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: Which of the following is the orthogonal trajectories of the family of curves y^(5) = kx^(4)? There…

A: To find orthogonal trajectories in the curve substitute -dx/dy for dy/dx in the differential…

Q: Find the value of c such that the line y = (1/6)x + (3/2) is tangent to the curve y = c(sqrt(x)).

A: Solution: Y1=16x+32Y2=cx

Q: Find the linear approximation to the equation f(x, y) = 3, xy at the point (8, 4, 6), and use it to…

A: To find the linear approximation to the equation at point (8,4) Given that f(x,y)=3√(xy)/8

Q: Show that the square of the length of the subtangent at any point on the curve by2=(x+a)3 (b is not…

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Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + B.

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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: YouTrylt 2 Find the linear approximation of the function f(x,y) =In(x- 3y) (7,2) at and use it to…

A: Please rate and feel free to ask any query about any part of the question.  Thanks

Q: 3. Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle…

A: given family of parabolas y2=cx at angle θ=60° claim- find the family of oblique trajectories that…

Q: Find the tangent/sto the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x – 4y = 2.

A: The equation of the parabola is given as  x+2y2+2x-y-3=0. On simplifying,…

Q: Find the orthogonal trajectories of the family of curves x²- y2=C² A) x- y=C (B xy3=C xy=C D…

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Q: Given the function z = = f(x,y) = 2y³ -5xy-3x²+2, find the equation of the tangent plane at (1,-1),…

A: Given problem:- Given the function z  = f(x, y) = 2y³ −5xy-3x²+2, find the equation of the tangent…

Q: The orthogonal trajectories of the family of curves y= cx² is A x=ky? B 2x2+y2 = k © x2 = ky? x2…

A: The given family of curve y=cx2

Q: Find the length of one branch of the curve ay? = x3 from x = 0 and x = 5a. 4.

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Q: Find the linear approximation to the equation f(x, y) xy at the point (6,2,6), and use it to 3 = 3…

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Q: find the value of c that the line y=3/2x+6 is tangent to y=c(sqr-root x)  c=

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Q: Find the orthog onal trajectories of the circles x+y - ay = 0, where a is a parameter.

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Q: Find the orthogonal trajectories of the family of curves y = kx'. = C (C) 3 y³ +x? = C (D) 3 y³ + 3…

A: Given y5=kx5 To find the orthogonal trajectory

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

A: Given that, y=cx.

Q: Find the points on the curve C where the tangent is horizontal C: x = t + 6t, y = t' – 3t. O A.…

A: First we have to calculate dy/dt then,we have to find out the value of t for which dy/dt =0 To find…

Q: Given f(x,y) = sqrt(x^2+4y^2) at point (3,2) find the linearization and use it to approximate…

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Q: Given the parabola: x2+12y=0 and the tangent line x+y-3=0, find the point of tangency

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Q: Find the point at which the line 7(t) = +t intersects the yz plane.

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Q: Find the linear approximation of y = V1+ x at x = 0 and use it to approximate V1.05 7.

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Q: Find the length of the curve given by F() =(6t, 12/7, 3Int) for 1<tse. О 8е-4 О 2e-1 O 4e-2 O e O…

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Q: Which of the following two families of curves are orthogonal trajectories of each other? 1, .y = e,…

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Q: Find the point at which the line 7(t) +t intersects the | xz plane.

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Q: In the xy-plane, the line x + y = k, where k is a constant, is tangent to the graph of y = x^2 + 3x…

A: Given line is x + y = k, where k is a constant it is tangent to the graph of y = x^2 + 3x + 1…

Q: The curve y = ax? + bx +c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A: Explanation of the answer is as follows

Q: The tangent line to the graph of y = In(2x) is perpendicular to a + 4y = 1 at the point where Select…

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Q: Find the linear approximation to the equation f(x, y) = 2, at the point (4,6,4), and use it to %3D…

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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: 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: The orthogonal trajectories of the family of curves y= cx² is A x² = ky? x² +2y² =k В © x=ky? D 2x2+…

A: In this question we have to find the orthogonal trajectories of the family of the curves y=cx2

Q: 3. Find the length of the curve y = x - In a, 1< x < 4.

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: The tangent line to the graph of y = nz is perpendicular to the line z = 7 at the point where Select…

A: Line x = 7 is perpendicular to x axis. A line perpendicular to this will be parallel to x axis.…

Q: Find a function f:R² → R, its tangent plane at the point (1; 1; f(1; 1)) is given by -2x – 9y – z+8…

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