Find the length of the curve r= 1+ sin(20) Oses- /20

Q: At what points (r, 0) on this curve are the tangent lines horizontal? Use 0 < 0 < 2n. r = 1- sin 0

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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: Find an equation of the tangent line to the graph of sin(x+ y)= y´ cos x at (7, 0) and graph this…

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Q: |x = 3 sin´ (3t ) +1 ;teR = 2 cos (3t)–1

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Q: Find an equation of the tangent line to the curve at the given point. y = 5e* cos(x), (0, 5) y =

A: Given equation - y = 5excosx           .............................(1)Let the equation of the…

Q: Show that the point (2, 4) lies on the curve x3 + y3 - 9xy = 0. Then find the tangent line and…

A: Given: f(x, y) = x3 + y3 - 9xy = 0 To find:  Equation of tangent and normal to the curve at point…

Q: Of the infinitely many lines that are tangent to the curve  y = −3 sin(x)  and pass through the…

A: Given :    Of the infinitely many lines, that are tangent to the curve y = −3 sin(x)  and pass…

Q: Find an equation of the tangent line to the curve at the given point. y = sin(2x) + sin²(2x), (0, 0)

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Q: (a) Find the equation of the tangent line to the curvey = 2 sec x – 4 cos x at the point (, 2) %3D

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

Q: (a) Find the equation of the tangent line to the curvey 2 sec x- 4 cos x at the point , 2) %3D

A: Since you have posted a multiple  question according to guildlines I will solve first…

Q: Find an equation of the tangent line to the astroid at the (3√3, 1).   x2/3 + y2/3 = 4

A: Given an astroid equation find the equation of tangent at a point.

Q: Find an equation of the tangent line at the point specified.

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Q: What is the equation of the line tangent to the curve ev + cos(x) = 1 at the point %3| 2 y = x + y =…

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Q: Plot the astroid x = cos3 θ, y = sin3 θ and find the equation of the tangent line at θ = π/3 .

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Q: The slope of the tangent line to the curve y at the point (2, 1) is: The equation of this tangent…

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Q: If the normal to the curve y-f(x) at the point(3,4) makes an angle of Pi with the positive x-axis…

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Q: sin(7x) + sin2(7x),  (0, 0

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Q: Find an equation of the tangent line to the curve at the given point. y = 3ex cos(x), (0,3) %3D

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Q: 3. Find the equations of the tangent and normal lines to the curve f(x) = /2* +cos(x*) at(0,/2).…

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Q: Graph the curve x = cos t + 2 cos 2t y = sin t + 2 sin 2t to discover where it crosses itself.…

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Q: Find the slope of the tangent line to the 1 cos(t) at the point parametric curve ly = 3 sin(t)…

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Q: Show that the curve  x = 3 cos(t), y = 5 sin(t) cos(t)  has two tangents at (0, 0) and find their…

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Q: Use four equal-length Hermite curves to interpolate y = sin(x) in the interval [0,2π].

A: To interpolate y = sin(x) in the interval [0,2π] using four equal-length Hermite curves

Q: 1. Use four equal-length Hermite curves to interpolate y = sin(x) in the interval [0, 2r].

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Q: Find the slope of the tangent line to the curve 5 sin(æ) + 3 cos(y) – 4 sin(x) cos(y) + x = 7n at…

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Q: what is the equation of the tangent line to the graph of xsin(xy) = (√2)/2 at the point (1, pi/4)

A: iven:xsin(xy)=12

Q: Find the slope of the Curve r=-I+Sine atthe points 8=0,T-

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Q: Find the arc length of the graph of the functionf(x) =x^3/2 fromx= 0 tox= 4.

A: Given,        The arc length of the graph of the function fx=x32 from x=0 to x=4.We know that,…

Q: 5. Find the slope of the tangent line to the graph of r = 2-2 cos 0 when 0

A: Given equation of the curve - r = 2-2cosθSlope of the tangent to the curve is given by drdθ,drdθ =…

Q: Find the slope of the tangent line to the curve 2xy + 4* = y2 – tan(2x) at the point (0, 1). Give…

A: Given curve:      2xy + 4x = y2 - tan2x   slope of the tangent line  =  ?

Q: Find the equation – in any convenient form – of the tangent plane to z = x² sin(x+2y) at the point…

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

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Q: Compute the length of the curve r-4 sin 26 for Approximate to three decima places.

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Q: Find an equation of the tangent line to the curve at the given point. y = sin(4x) + sin2(4x), (0, 0)

A: general equation of line is:             y = m(x) + c where, m = slope of line    and, c = constant

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: the length of the curve y = coshx 1<= x <=2 is sish (2) - sinh(1) Select one: True False

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Q: Find an equation of the tangent line at the point indicated.

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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 equation for the line tangent to the curve 2 sin(20) - cos(30), y- sin(40) + 3 cos 0 at 0 =…

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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 line to the graph of r = 2-2 cos e when 0 %3D

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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 an equation of the tangent line to the curve at the given point. y = 3/sinx+cosx,    P = (0,…

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Q: Find the slope of the tangent line to the polar curve =1- sin 40 at 0 = 4

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Q: Find an equation of the tangent line to the graph of y = arcsin(2x) at the point 2/2 4

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Q: Kappa Curve: x²y² + y* = 2x² %3D

A: We are asked to find the slope of the tangent line at the given point

Q: Of the infinitely tmany lines that are tangent to the curve y=-4 sin(x) and pass through the origin,…

A: Answer is mentioned below

Q: Find the slope of the tangent line to the curve  5 sin(x) + 2 cos (y) - 5 sin(x) cos(y) + x =5π at…

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Q: The curve defined by the equation x^2+y^2=(2x^2+2y^2-x)^2 is called a cardioid. Find the equation of…

A: consider the given equation, x2+y2=2x2+2y2-x2 Use implicit differentiation method and differentiate…

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.