3. What is the length of the curve r = cos3 (-) where 0 < 0 <- 4

Q: 4. Suppose the point is on the curve sinx Siny - c, where C is a constant. Use =C, 3'4 the tangent…

A: To find the tangent line approcimation on the following curve

Q: 4. Find the length of arc of the curve x3 + y3 = 1 in the first quadrant from the point where x = to…

A: If a function f(x) is defined over an interval [a,b], then the formula for arc length is: Formulae…

Q: 1. Find the length of arc of the curve y = () from the point where x = to the point where x = 2.

A:

Q: 9. Find the slope of the tangent line to the graph of f (x) = sin (cos 2x) at x = 1 A. -2(sin 2)(cos…

A: we have to find the slope of the tangent line to the graph of fx=sincos 2x at x=1

Q: what is the arc lenght of  the curve y=ln(sinx) between th points x=pi/3 x = 2pi/3 ?

A:

Q: The slope of the tangent line to the curve r=cos20 at 0= 1/4is none of these O-V3 0 1 O (-1)/V3

A: As we know that; The slope of the tangent line to the polar curve at the given point is equal to the…

Q: Find the length of the arc of the curve y =: +e*) from x = 0 to x =2.

A: y=ex+e-x2

Q: 9. Find the equation of tangent and normal for the curve xsin2y = ycos2x at 4'2

A:

Q: 3. Find the length of the curve y = In (cos x), 0 <x <

A: we have to find length of the curve

Q: A curve is defined by y=(1/3)sin(2x+1). Evaluate the angle between the tangent to the curve at x=2,…

A:

Q: (a) (., Consider the curve defined by ry = In(3x + sin(y)). Use implicit differenti- ation to find…

A: Consider the given equation of the curve, xy=ln3x+siny Use the implicit differentiation,…

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

A:

Q: Determine the equation of the tangent line to the graph of 3sin y – In(e secha) = tan- (x²y) + 3 at…

A: Given  : 3siny - ln(e sechx) = tan-1(x²y) + x/3

Q: 4. Find the exact arc length over the interval. a. x= from x = 2 to x = 3 16x2

A: Solution: 4 (a)   y= x6+816x2  from x=2 to x=3

Q: 2 4. Find the length of arc of the curve x3 + y3 = 1 in the first quadrant from the point where x =…

A:

Q: At what point on the interval (0, 7/2) does the tangent line to the curve = 3x + V3 cos x – sinx…

A:

Q: 34 10- Find equation of tangent line at the point (0, T) for Cos (7x- y) %3D 4y

A: Solved below

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].

A:

Q: 7- Find the leng thof the Curve arce 34 from to y=4

A:

Q: Find the exact length of the curve. y = 6 + cosh(3x), 0s x 8 중이nh(3) sinh(3)

A:

Q: Find an equation of the tangent line to the curve at the given point. y = 8ex cos(x), (0,8) y =…

A: Here y is given find.slope.from.it then solve as below

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…

A:

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: 3. Find the length of arc of the curve y = ln(secx) from x = 0 to x = 4

A:

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: 11. Find the equation of the tangent line to the curve 2 sin(ry) = x at the point (1, 7)

A: This curve is given by sin(xy)=x/√2                  sin⁡(xy)−x/ √2. =0  Inspecting the gradient at…

Q: 3. Find the arc length of the curve 24xy y+ 48 from y-2 to y-4 1 to from

A:

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

A:

Q: 5. Find the length of the arc for x = 3 - Jy from y = 0 to y = 4

A:

Q: 4- Find the question of the that is tangent to the curve y=-3 cos2x at x= π/6. Express with exact…

A:

Q: 4. Find the length of the arc of the curve 8y = x + 2x-2 from the point where x = 1 to the point %3D…

A:

Q: Find the exact length of the curve. x = 9 cos(t) - cos(9t), y = 9 sin(t) - sin(9r), Ostsn 9 cos (47)…

A:

Q: 1. If Y= 4 cos x + sin 2x, what is the slope of the curve when x=2.

A:

Q: Find the exact length of the curve defined by x = 3 cos t – cos 3t and y = 3 sin t – sin 3t on the…

A:

Q: 7. Find all x-coordinates where the tangent line to y = f(x) = sin(2x) – cos?(2x) is horizontal. -

A:

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

A:

Q: 61. Find the lines that are tangent and normal to the curve y = 2 tan( 7x/4) at x = 1. . %3D TTX

A: The given curve is  y = 2.tan(πx/4) Thr given point x = 1 At x = 1, y = 2*tan(π/4) y = 2 Point is =…

Q: 1. Find the point(s) if any where f has a horizontal tangent line. у %3D УЗх + 2 cos x 0<x < 2п

A:

Q: Find the length of arc of the curve y = - In x from x = 3 to x = 9. 9

A: f(x)=x29-lnx on the interval x=3 to x=9

Q: Find the arc length of the graph of x = 1 8y4 + 1 4y2 over the interval [1, 2].

A:

Q: Find the exact length of the curve x3 y = 6. 1 <x < 1. 2x Arc length

A: we have to find the arc length of the given curve

Q: 2. Find the arc length of the curve y = 16 from x-2 to x-3

A:

Q: 1- Find the equation of the tangent to the curve y= 2 sin x+ cos2x at the point x = n. 2- Find the…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: find the length of the arc of the curve from point k(8,8) to m( 1,5) X^2/3 -y = -4

A:

Q: what is the length of the curve y=1-cos(x) from x=0 to x=4pi

A: Given: y=1-cosx To find: We have to find the length of the given curve from x=0 to x=4π.

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.