15. Find the equation of the tangent line to the curve at point (0, In 2). y = In(e' + e4) O 2y + 5x = In 2 O 2y - 5x = 2 In2 %3D O 5x-2y 2 In 2 O 5x-2y = -In 2

Q: Q2 find the derivative of the following: 1) y = 2stn²(5x) ,2) y = Inx'n cosh 5x ,3) xsin¬14y = y…

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Q: find the differentials of the first and second orders u=xyz

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Q: 4) a²y=+52y =14 yat (2,1) Find equátion of tangent?

A: Equation of tangent  y-y1=m(x-x1) (x1,y1)are the points at which equation of tangent is to be…

Q: 9. From the differential equation sinh 2x, sketch some of the family of curves. %3D dx

A: Given differential equation, dydx=sinh(2x)dydx=e2x-e-2x2∫dy=∫e2x-e-2x2dxy=e2x+e-2x4+C

Q: What is the derivative of y = 34? a. y (4)(3**) b. y = 4x3 c. y = (4)(3*) In(3) d. y' = In(4x) + 34*…

A: We can answer all three subparts as below.

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A: We have to obtain the differential equation of the family of circles of fixed radius r with center…

Q: 1. Find the rate of y with respect to x at the point (5, 8) if 7y-ry 4. dy da

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Q: 6. Write down the differential, dy, of y = e3x.

A: to find the differential of y=e3x

Q: Obtain the differential equation for the family of circles with center on the line x = 8.

A: The general equation for a circle can be written as

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Q: From the differential equation by elimaniting arbitary constant y =ax'+ bx²

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Q: If f(x, y) = ln(x + y), then total derivative or total differential of f at x = 3 and y = 20 is : Y

A: Given data: The given expression for the function is f(x,y)=ln(x+y). The given value of x is x=3.…

Q: Find the differential equation of the family of circles with fixed radius, r=a+b,and tangent to the…

A: I am attaching image so that you understand each and every step.

Q: 1. Find the rate of y with respect to x at the point (1,8) if 7y² - xy³ = 4. dy dx

A: Given: 7y2-xy3=4 and Px,y=1,8   As we know that; The Power Law: ddxxn=nxn-1 The Product rule:…

Q: show Itat the differential equation メり dy - -2-ye" dx xーとリ Xe 29 its exact and find its Folution

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Q: 5. Obtain the Differential Equation from the family of vertical parabolas whose vertex is at (h,k).

A: Formation of the differential equation

Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ?

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Q: 3. Find the equation of the normal line to the curve f(x) = 6e2* cos x at the point (0,6).

A: Given: fx=6e2xcosx; 0,6 We know that for finding equation of normal at given point, we need to find…

Q: The differential equation ry" + 3y - 7y=seca is normal on any open interval not containing a = 0.…

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Q: tind the general solution of the secondorder constont coettident non-hama geneous iner differential…

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Q: 2.Evaluate the total derivative of u with respect to x for u = 6x²+4y² + 4z² when y = cosx and z =…

A: We have to find total derivative of u with respect to 'x'    where     u = 6 x2 + 4 y2 + 4 z2  Given…

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Q: 7. Find the differential dy of the function y = x (1-cos(x)). If the error in x is ", find the error…

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Q: 11. Find the length of the curve x = on the interval (2, 4] (integrate with respect to y) 12y3 un

A: Given that the function x =y55+112y3 Find the arc length of the graph of the given curve on the…

Q: 4. Get the exact a. dy = cos 2x dz differentials of y = (sin 2)² b. dy=sin 2z dz dy = sin 2x d.…

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Q: In (1 + 2), What is the derivative of y .? e2z %3D

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Q: Use linear approximation (or differentials) to estimate the given number. 3 а. V8.12

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: One of the methods to solve a differential equation is by separating the variables and integrating…

Q: Find the differential of the given functions. 1. y= x-2x² + 5 5. у 3 1- -s2

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Q: Suppose f is differential equation on (-inf, +inf), f(3)=12 and f'(3)=-2 use linear approximation to…

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Q: Find the equivalent differential equation for all tangent lines of the parabola y = x^2

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Q: 3. Obtain the differential equation of the family of straight lines passing through (0.1). SAdd File

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A: the given function for the thermal energy is E(t)=2.3t2-4.5 and as the thermometer is accurate to…

Q: The derivative of y= sech1(Inx)+esinh(3x) equals Select one: 1 3e sinh"(3x) O y' = - xInx/1-Inx…

A: Proceed as shown below...

Q: 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 =…

A: (1) given equation is                                              2x2+y22=25x2-y2,   at (3, 1)…

Q: 1 By considering the secant through the points where x = 1.2 and x = instantaneous rate of change of…

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Q: If fex, yJ-o find dy /af partial derivative off dx

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Q: Find dy ax oy Impticit dipTErentation 3. Find 2nd derivative

A: 1) The given equation is 2x2+2y2=17 Differentiate both sides of given equation 2x2+2y2=17 with…

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Q: 4. Differentiate y with respect to x. y = (In Vcosh3x)(sinh(2x + 1) ex+1)

A: The given function is: y=lncosh (3x)sinh-1(2x+1)

Q: Find y(1) for y" = - 4z - 4y, X, = 0, yo = 0, z, = 1, with step length 0.1 using Euler method (2nd…

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Q: 13. Obtain the differential equation of the family of straight lines at a fixed distance p from

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Q: A/ By using Linear equation solve the first order differential uation y' + sec(x)y= cos(x)

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Q: What is the differential equation of family of parabolas with vertex on the x – axis and axis…

A: General equation of parabola parallel to y-axis and having center (h, k) and having distance 'a'…

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Q: Calculate the truncation error to solve the differential equation: Yi+1¬Yi = Xị → (*) Ax dy Instead…

A: Follow the following solutions to get the complete correct answer.