Use a linear approximation to estimate V29. Show the work. Do not round your

Q: Find the condition that the line ax+by=1 may be a normal to the curve an-1y=xn

A: To find the condition of line ax + by = 1 which is normal to the curve a^(n-1) y = x^n

Q: What is the normal line to the curve 9x4 + 4y = 36 at (0,3) ?

A:

Q: Show that the square of the length of subtangent at any point on the curve by2=(x+a)2 (b is not…

A: Here given curve  by2=x+a2

Q: Find the orthogonal trajectories for the family of curves, sin? y C In x.

A:

Q: Find the orthogonal trajectories of the family of curves y^3 = 3(? − ?). Draw a few representative…

A: We will find out the required solution.

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

A:

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

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Q: Estimate using the Linear Approximation or linearization, and use a calculator to estimate the…

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Q: Show that the normal line at any point of the circle x2 + y2 = a2 passes through the origin.

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Q: 5. Using tangent line approximation, approximate the value of: a. V9 b. 3.012 – 4(3.01) + 7

A: The objective is to tangent line approximation to approximate the value of 3.012-43.01+7

Q: Find an equation of the normal line to the curve  y = x  that is parallel to the line  4x + y = 1.

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Q: Use an appropriate local linear approximation to estimate the value (2.03)^3

A:

Q: Find the orthogonal compliment to S span{ 0 }. ||

A: To find the orthogonal complement to S spanned by two vectors .

Q: Find the length of the following curve. y = 2x + 4 on 3-2, 24 (Use calculus.)

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Q: Find the orthogonal trajectories of the family of curves.

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Q: y = 3x – 1 + Ce-3x | x = Cey?

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Q: Estimate the cubed root of 28 using a linear approximation

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Q: estimate using the Linear Approximation and find the error using a calculator. 9^1/3 − 2

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Q: Calculate the length of the tangent line, normal line, sub-tangent and subnormal from: a. 4x² + 9y =…

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Q: Use a linear approximation to estimate the value of the 5th root of 30

A: To find: The fifth root of 30 by using linear approximation: Concept used: Linear approximation of…

Q: Find an equation of the normal line to the parabola  y = x2 − 4x + 1  that is parallel to the line…

A:

Q: For a χ2-curve with 19 degrees of freedom, find the χ2-value that has area a. 0.025 to its right. b.…

A: a) Degrees of freedom is 19 The chi-square value that has area 0.025 to its right is given below:…

Q: Given y=[cube rt]x, find the local linear approximation for y near x=-8 and use it to estimate the…

A: Given: The function y=x3 To find: The local linear approximation for y near x=-8 and using this…

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 least squares quadratic & bj xj which best fits curve Y = sin(x)

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Q: Find an equation of the normal line to the parabola y = x2 – 8x + 4 that is parallel to the line x –…

A: Let the equation of the normal line in the slope-intercept form is, y=mx+c where m is the slower and…

Q: Find an equation of the normal line to the curve of y = Vx that is parallel to the line 6x + y = 1.…

A: Given that: The curve y = x parallel to the line 6x + y = 1 To find: The equation of normal line to…

Q: Find an equation of the normal line to the parabola y = x 2 - 5 x + 4 that is parallel to the line…

A: Given:       y=x2-5x+4 is parallel to the line x-3y=5.

Q: Use Simpson’s Rule with n  =6  to estimate the length of the curve x  =t - et -6<t<6

A:

Q: Distinguish briefly the Skewness and kurtosis

A: Skewness is a measure of symmetry where symmetry means equal proportion to the left and right to the…

Q: Find the orthogonal trajectories of

A: Given,          y=ax2+4ax+4a, where a being paarameter.

Q: Find the equation of the normal line to the curve y=(1+2x)^2 at (2,25)

A: Equation of a normal line to the curve y=f(x) at point x1,y1 is given by y-y1=-1dydx(x1,y1)x-x1.…

Q: Show that the slope of the secant line for f(x) = x 3 - 2x over[5,x] is equal to x 2 + 5x + 23. Use…

A: Given: y=fx=x3-2x; 5,x we know that slopem of secant for any given functionfx over a,b is given by…

Q: Find an equation of each normal line to the curve y = x³ – 3x that is parallel to the line 2x + 18y…

A: Solve the above question.

Q: Find the condition that the line ax+by=1vmay be a normal to the curve an-1 y=xn

A: follow next step

Q: determine the equation of the orthogonal trajectories of the following families curves: Straight…

A:

Q: Find the equation of the normal line at 2 x = 0 to the curve, y + 0. x – 3 %3D -

A: Given: Equation of the curve…

Q: Estimate 3√9 using a linear approximation at a=8.

A:

Q: Find an equation of the normal line to the curve y= sqrt(x) that is parallel to to the line 2x+y=1.

A: The equation of the curve is y=x and the equation of the line parallel to the normal line is 2x+y=1.…

Q: Use local linear approximation to estimate V(7.88)4. 3

A: Let, f(x)=x43 To linear approximation of f(x) around a=8. The formula for linear approximation is:…

Q: Find the length of the the interval -2sxs-1. y = L, V3t² – 1 dt curve in

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Q: Find the slope of the normal line to curve x=4sint, π y=cos2t when t=-

A: Given that x=4 sin ty=cos 2t Find the slope of the normal at t=π4 find the slope of normal and then…

Q: Make two separate plots of the function E- 2sin(1.5x) in the domain -3Sx53 and -3 sys3. 3-D surface…

A:

Q: What is the standard linear approximation?

A: A linear approximation is an approximation of a general function using a linear function. They are…

Q: A straight-line fit y3 = e12), could be obtained with:

A:

Q: Determine the length of the latus rectum of the curve y² = 8x

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Q: Compute the length of the curve: f (x) = x² 2x, 0<x<2

A: Given:- f(x) =x2 -2x  To find:-  Length of curve over interval [0, 2]

Q: Determine the equation of the orthogonal trajectories of the following families curves: circles…

A:

Q: Let x = t3-3t2 and y = t2-4t, find when all horizontal and vertical tangent's occu

A:

Q: Find the normal form of the line 3x + 4y – 10 = 0 and its where distance from the origin.

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.