1- Find the equation of the tangent to the 2(x2 + y2)2 25(x2 - y?) at (3,1) 2- Find dy/dx for y = In(tan(2x²)) 3- Find dy/dx for y log2(1- sin3 (3x2) 4- Find dy/dx for y = 3(sin"(e-3**) dy = 3[(sin-(e-3*" )I dx "In3 2(sin-"(e-3x")- V1-e-6x2

Q: 7- cos y dx + (x siny - cos²y)dy = 0

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Q: 3. Find the differential equation of a family of circles with center on the y-axis.

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Q: 4. Form the differential equation representing the family of hyperbola having the center at the…

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Q: Obtain the differential equation of the family of circles with center at point (h,k) and radius r.…

A: The equation of the circle having a center (h, K) and radius and radius r is given by:…

Q: Obtain the differential equation of the family of curves described and sketch some members of the…

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Q: 1- Find the equation of the tangent to the curve y = 2 sin x+ cos2x at the point x = n. 2- Find the…

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Q: 31+2 dy - of the function y= dt 7. Find +4 dy of the function y = 5 tan (6x)+ log, (36x² + dx 8.…

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Q: 1. Find the differential equation of the family of circles of fixed radius r with centers on the…

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Q: Find the differential equation of the family of circles of fixed radius r with center on the x-axis.

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Q: 23 Find dy/dx on the graph y3 sec/x2 + y2 = cos2x at point (1, 2).

A: Use product and chain ruleof differentiation at given value

Q: The slope of the tangent line to the curve r=cos20 at 0= 1/4is none of these O-V3 0 1 O (-1)/V3

A: As we know that; The slope of the tangent line to the polar curve at the given point is equal to the…

Q: 2. What is the largest possible area of a triangle with its base on the x-axis between x= 0 and…

A: The given curve is y=sinx. To find the largest possible area of the triangle with its base on the…

Q: 57 6. Find an equation of the tangent line to y = f(x) = cos²(x) at %3D

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Q: Find the differential equations of the families of curves: Parabolas with vertex on the x-axis and…

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Q: a. Circle of radius 1 and centers on the line y = x

A: The solution is given as

Q: Find the differential equation of the family of parabolas whose foci are located at (a, 0) with a…

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Q: Obtain the differential equation of the family of curves as described. Draw some representative…

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Q: 8. Find the length of the curve y = e on the interval 0, ln 2| %3D

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Q: SOLVE FOR THE DIFFERENTIAL EQUATION OF THE GIVEN FAMILY OF CURVES. 1. Circles with fixed radius “R"…

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Q: A nomal is drawn at a point P(x, y) of a curve, it meets the x-axis at Q. If PQ is of constant…

A: Equation of normal at the point P(x,y) to the curve is Y-y=-dxdy(X-x). ⇒X=x+ydydx Thus,…

Q: Show that the solution of the differential equation (1–x*) = 2x(1+ y). dx 1+x given that y=1 when…

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Q: 1- Find the equation of the tangent to the curve y = 2 sinx+ cos2x at the point x n. 2- Find the…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: obtain the differential equation of the family of curves described and sketch some members of the…

A: Recall that the order of a differential equation of a given relation is the number of arbitrary…

Q: Find a differential equation of the family of parabolas with vertex on the y-axis, with axis…

A: Let the vertex is at a point (0,k). Then, the expression of the family of parabolas with axis…

Q: x(1- siny)dy = (cosx cosx – cosy -y)dx. 0.

A: The given differential equation is x1-sinydy =cosx-cosy-ydxyπ2=0

Q: a)  Use the hyperbolic identity sech^2(x)  = 1 - tanh^2(x)  to solve 4tanh^2 (x)  + sech^2(x)  =3…

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Q: Find the differential equation of the family of cuves and draw at least three members of the family…

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Q: 1+ tanx y = logy 1- tanx prove that 9 = sec2x dy dx

A: Given,           y=log1+tanx1-tanx

Q: 2. Use implicit differentiation to find dy/dx: e"y+ In(arcsin 2y) = 3ª ln y + 5.

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Q: Find the differential equation characterizing the family of curves described. a. Tangent to ky=x²

A: Tangent to the curve

Q: Prove first that sinx siny dx - cosx cosy dy =0 is an exact differential equation then determine its…

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Q: Obtain the differential equation of the family of curves described below. a. Circle of radius 1 and…

A: a) Given radius of circle r= 1 and center lies on y=x linewe know that circle equation is…

Q: 2. Find using implicit differentiation. Enclose final answers. dx (a) 4x³y² + x¹y³ = x + y = 0 (b) x…

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Q: Obtain the differential equation of the family of curves described and sketch some members of the…

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Q: Obtain the differential equation: Parabolas with vertex on the y-axis, with axis parallel to the…

A: This is a differential equation problem

Q: Find the differential equation of a family of circles of fixed radius p with centers on the x-axis.

A: The objective of the question is determine the differential equation of a family of circles of fixed…

Q: Find a differential equation of the family of circles with center on the line y = -x, and passing…

A: Let, the equation of the family of circles with center         on the line y=-x & passing…

Q: Parabolas with axis parallel to the y-axis

A: Equation of parabola parallel to y-axis and having center(h,k) and having distance a from vertex to…

Q: Find the Differential Equation of the Families of Circles with center (2,k) and with radius r.

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Q: 1: Find the derivatives of: 1+ tanh x a) y = In ソ= %3D 1- tanh x b) 2 y= cosh? 1-x? 1-x

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Q: Find the differential equation of all family of circles in which the center lies on the line y = -x…

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Q: Find the differential equation of Parabolas with vertex on the x-axis, with axis parallel to the…

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Q: Find the differential equation of family of parabolas with axis parallel to the x-axis and with…

A: The general equation of family of parabolas with axis parallel to the x-axis, with a vertex at a…

Q: 27. Obtain the differential equation having the solution as the equation representing all circles of…

A: The differential equation of all circles of radius 1 and centers on  y=x

Q: 5. Using the method of stationary Phase find the leading term behavior of cos (xt*)dt as X 00.

A: To find the leading term behaviour of a function we need to analyze the asymptotic behaviour of the…

Q: 8. (a) Evaluate the indefinite integral dx sinhx+coshx e 4x (b) Find and simplify the derivative of…

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Q: 1. S(esin *cos x – acos 2x sin 2x)dx 2. S(etan x sec x- esecx tanx)sec x dx 3. S dx xvax - 16 3x-2…

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Q: 2. Find the linear approximation to y = sinh (3x) at x=2. State your answer in both exact form and…

A: Find the linear approximation of f(x) at a point x=2

Q: B. Find the differential equations of the families of curves. 6. Parabolas with vertex on the x-axis…

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Q: SOLVE FOR THE DIFFERENTIAL EQUATION OF THE GIVEN FAMILY OF CURVES. 1. Parabolas with vertex and…

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