Set up an intergal of the Curve for the length 3T Y%3DZE* sin (x), O4 xE 2

Q: Find the exact length of the curve. y = ln(Sec x),   0≤ x ≤ π/4

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Q: Use implicit differentiation to find dydxdydx without first solving for y. x^4+y^4=−2 dy/dx=?

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Q: The linear approximation at x = 0 to sin(2x) is A + Bx where A is: Preview and where B is: Preview

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Q: Find the slope of the tangent line. y = cos3x at x= -5pie/12

A: Given:     y = cos3x      At x = -5π/12

Q: EVaLuate W= X -*-cos't ,y=cost sint

A:

Q: Find the curve y(x) that minimizes the I Cy) = S. cos x)+ ]2 Cunc tonal %3D

A: solution:-Given I=∫1+cosx+y121/2using Euler's equation ∂f∂y-ddx∂f∂y'=0sincef=1+cosx+y121/2is…

Q: se implicit differentiaion to find dy/dx for the curve below. 1. xy3 + 4x2 = tan y2 + 3

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Q: he tangent line to y = f(1) at (-3,9) passes through the point (9,-3). Compute the following.

A: The slope of the line passing through the points, (x1,y1) and (x2,y2) is given by .

Q: Find the slope of the tangent line for the curve r = 4 – 5 cos 0 when 0 6 %3D -

A: r=4-5cosθ

Q: Find the equation of the tangent line at the given value of x on the curve. 3y +xy-y%3D375X"; x-1…

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Q: Find the length of the curve y=ln(sec(x)), 0≤x≤π/4.

A: please see the explanation below

Q: Find a point on the folium x3 + y3 = 3xy other than the origin at which the tangent line is…

A: Implicit differentiating both sides of the equation x3+y3=3xy with respect to x. Use power rule of…

Q: Find the question of the that is tangent to the curve y=-3 cos2x at x= n/6. Express with exact…

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Q: Find the equation of the line tangent to the graph of y = arctan (sinh(r)) at z = 0. %3!

A: Given: y=arctan(sinh(x)) Since, ddxtan-1fx = 11+fx2f'x Therefore, dydx=11+sinh2xcoshx

Q: it Z = exY , where : x= Incutv) and y = tan () %3D find a) du శ్రీశర శశ్ర

A: Given,  z=exy ; where x=lnu+v and y=tanuv To find: partial derivatives

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: Evaluate 112x C: arc on y = x5/2 from (0, 0) to (4, 32) (2x - y) dx + (x + 3y) dy.

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Q: Find the length of the curve defined by y = 3 ln from x = 8 to x = 9.

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Q: The tangent of the curve x^2+y^2--7 * 2xy3DO at the point (1,1), is a. y-2-х. О b. y=x-2. O С.…

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Q: The linear approximation at x = 0 to sin(3x) is A + Bx where A is: Preview and where B is: Preview

A: Given function:

Q: Find the tangent line at (1, 0) of the curve xe^y = 2 sin(xy) + cos y.

A: Slope of the tangent is given by the derivative of the function at that point. So first we will find…

Q: Find the slope of the tangent line to the path of a carnival ridex=8 cos(t) + sin(81), y = 8 sin(t)…

A: The slope of the tangent is dydx.

Q: Use the composite trapezoidal rule with the step length h = 0.1 to evaluate sin x -dx, in six…

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Q: Find the length of the curve f(x) = ln(sin x), 0 ≤x ≤π/6.

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

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Q: 2. Find the length of the curve: y = 2 In (sin (x)):sxS*

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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: 2. Find the length of the curve: y = 2 In (sin (÷x)); -< x

A:

Q: Find the linear approximation to y=arcsinh(2x) at x=6.

A: Given:y=arcsinh(2x) and x0=6To find:The linear approximation to y=arcsinh(2x) at x0=6

Q: B) Find the skpe of the Ine tangen to the curve y = sin-x at the poit

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Q: 8. Find a parameterization of the tangent line to r(t) = (cos(t), sin(2t)) at the point

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Q: ) If y = cos2x + 2cosx for 0 < x < 2n. Find the points at which the tangent line is horizontal.

A: Given function is y=cos2x+2cosx for 0≤x≤2π. To find the points at which the tangent line is…

Q: Find the slope of the tangent line to the curve 2 sin(z) +4cos(y) –- 3 sin(z) cos(y) + z = 7x at the…

A: The objective is to find the slope of tangent line to the curve at the point (7π, 3π/2).

Q: Evaluate the length of the curve: y = 3x + sinx, 0 ≤ x ≤ 1.

A: Let L be the length of curve  F(x) = 3x + sinx

Q: Use the composite trapezoidal rule with the step length h = 0.1 to evaluate sin x = 5.² in six…

A: Given integral is ∫0πsinxxdx. We have to evaluate the given integral by using composite trapezoidal…

Q: Find the equation of the tangent line to the graph of F(r)= 2z²+2r+1 evi dy at r 0. sech z

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Q: The equation of tangent line to y =2rsinx at the point (T) is : Select one: a. y=2x O by=-2x+27 O…

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Q: Find the slope of the tangent line to the curve 5 sin(x) + 5 cos(y) – 6 sin(x) cos(y) + x = 6T at…

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Q: Find an equalion of the tangent line to the curve at the given point. y= (1+x) cos x, Co, 1)

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Q: Determine the equation of the tangent line to the graph of g(x) = Sm, [1 – sin(ne')]dt at %3D In x…

A: We have to find the equation of the tangent line to the graph of gx=∫lnx01-sinπetdt at the point…

Q: Find the slope of tangent to the curve y=sin 4x +3x at (5, 35). None O 7 O 3

A: Note :- Steps to find slope :- 1) Find the first derivative of f(x). 2) Plug x value of the…

Q: Find the length of the curve.   y = 2 In (Sin 1/2 x) , π /3 ≤x ≤ π

A: y=2lnsin12x,  π3≤x≤π Differentiating with respect to x, we get dydx=2·1sin12x·ddxsin12x…

Q: Find the slope of the tangent to the curve y-x cos 3x at *- O al o Ob) 1 Od) 3

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Q: Determine the length of the curve TC f(x) = In[sec(x)],0 < x < 4

A: The given curve is- f(x)=lnsec(x)Interval 0≤x≤π4We need to determine the length of the given…

Q: Consider the curve satisfying y" = 6x and is tangent to the line y = 5– 3x at x = 1. What is y' (2)?…

A: Given: y''=6xand tangent to the line y=5-3x at x=1To find y'(2)=?

Q: Find the slope of the tangent line to the curve 5 sin(z) + 4 cos(y)- 5 sin(z) cos(y) + z = 3x at the…

A: Consider the curve  5sinx+4cosy−5sinxcosy+x=3π

Q: Find the length of the curve y = ln (sin x), π/6 ≤ x ≤ π/2

A: Given y = ln (sin x), π6≤x≤π2

Q: Find the length of the curve y= ln sec x, Oln OIn 2+y3 V3 OIn 2+/3 OIn V3 2-V3

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Q: Find t6e eavation of tangent ine of fcx) = X+) at X=2 X-3

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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.