Let a>0. The line y=TX-2 is an oblique asymptote to the curve y=Vax? +1.tan-lx at +o. Find the value of a. Your answer should be an integer.

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A: given curve x=lnt  , y=et

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Q: For what values of a are the graphs of y = a* and y = 1 +x tangent at x = 0? Enter the exact answer.

A: Please see the explanation below

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A: We have to find the derivative of the function first.

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A: Find the equation of line

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Q: The line y = mx + 1 is a tangent to the curve y2 = 4x .Find the value of m

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Q: Q4:A/ Find the length of an arc of the curve y = (1/6) x + (1/2) x from x = 1 to x = 2.

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

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Q: Given the curve: y = 4cos3x – 3cosx, find the following values of x (from 0 to 2pi radians) when a.…

A: see the attachments

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A: Differentiate at given point

Q: 1. In the open interval (0, T1/2) , find the point where the slope of the curve is 4? y = tan x

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A: This is application of derivative problem

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A: We will find the length of the curve from the graph of the given function as shown below

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Q: The curve y = sin'x has a slope of %3D Select one: a. at æ = ± O b. Never O c. at x = 0

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

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A: Find the arclength of the curve y=3/2x^2/3 for x=1 to x=8.

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Q: Find the exact length of the curve. y = In(cos(x)), 0 s xs- TO 6. Need Help? Read It

A: Given problem:- Find the exact length of the curve.   y = In(cos(x)),   [0, π/6]

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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.