) Sketch the curve: f(x) = x* – 6x²

Q: Find the length of the curve on y=2x^(3/2) from x=0 to x=1

A: Explanation of the solution is given below...

Q: Find the exact length of the curve. y = 3 + 2x^(3/2), 0 less than x less than 1

A:

Q: Does the curve y = x4 - 2x2 + 2 have any horizontal tangents? If so, where?

A: Consider the given function y=x4-2x2+2.

Q: Find the arclength of y = 2x2/3 from x is greater than or equal to 1 and less than or equal to 2

A: The arc length of the function y=2x23 between x=1 to x=2.

Q: Find equation of the tan gent line to the curve f(x) = /16–4x at (3,2) a)

A: To Determine: a. Find the equation tangent line to the curve

Q: Use the guidelines of curve sketching to sketch the curve y = 1-x2 %3D

A: Given: y=x1-x2

Q: Find the exact length of the curve. 1 y = 4 -x² - In(x), 1< x < 8 2

A:

Q: Find an equation of the tangent plane to the graph of f(x, y) = xy3 + x2at (2, -2, f (2, -2)).

A: fx, y=xy3+x2 Partially differentiating with respect to x, keeping y as constant, we get fxx,…

Q: Sketch the following curve y f(x, y) = x² + 1

A: Given function, fx,y=yx2+1 To sketch the curve of the function.

Q: Find the exact length of the curve. y = In(1-x), 0sxs 8.

A: Given that: y=ln 1-x2, 0≤x≤18

Q: Find the length of the curve y = In(1-2) over the interval

A:

Q: What is the length of the curve y = sqrt(4-x2) from x = -2 to x = 1?

A: y=4-x2 Differentiating with respect to x, we get dydx=124-x2·d4-x2dx   ∵dxdx=12x=124-x2·0-2x=-x4-x2

Q: Find the equation of the tangent f (x) = 4x – 8/a at a = 16. %3D %3D -

A: Given: Curve f(x)=4x-8x to find tangent at x=16

Q: (x – 2)2 + y² = c² %3D

A:

Q: Find the length of the curve y = x2 from x = 0 to x = 7.

A:

Q: Find the exact length of the curve. 는x - - In(x), 1<x<6 4 2

A:

Q: 4. What is the area of the largest rectangle that can be insribed in the first quadrant under the…

A:

Q: Find the length of the curve y = In (1 – 2*) over the interval [-,].

A:

Q: Find the length of the curve y = In(1 – x), 0sxs.

A: Given: y=ln(1−x2)0≤x≤12

Q: Find the length of the curve y=x^3/2 from (1,1) to (2,2squareroot2)

A:

Q: Find an equation of the tangent plane to the graph of f(x, y) = 4x² - 7xy² at the point (7, 8). z =

A:

Q: Use calculus to find the point on the curve y = 3x−1 that is closest to the point (2, 0).

A:

Q: Determine the values of x where a curve y=x³-3x²-9x+12 has horizontal tangent lines

A: Given,y=x3-3x2-9x+12differentiating both the sides w.r.t. xdydx=ddxx3-3x2-9x+12dydx=3x2-6x-9

Q: Find the length of the curve y = x3/2 from x = 0 to x = 3.

A:

Q: Determine the points where the curve f(x) = 2x3 + 3x2 – 36x + 1 has a horizontal tangent. -

A:

Q: a) Calculate the length of the curve defined by x = -3 )on the interval 1 sys9.

A: (a) Given that, x = 13 y (y-3) on the interval 1 ≤ y ≤ 9   We have to calculate the length of the…

Q: + 2 Find the length of the curve y = from the point where a = 1 to the point where x = 2.

A: The length s of a curve with the function y=f(x) for the interval of x from a to b is given by the…

Q: Use the guideline of this section to sketch the curve 1. y = 1 + 1/x + 1/(x ^ 2)

A: To Sketch: y=1+1x+1x2 Explanation: (a). Domain and Range y=1+1x+1x2is defined everywhere except…

Q: Find the length of the curve y x7 from ¤ = 0 to x = 15. 2/3

A:

Q: Let C be the curve y = 2/r for 1.3 <x < 3.2.

A: Given that: y=2x

Q: 2. Use the guidelines to sketch the curve. Y In x x²

A: The given function is: y=ln xx2 Note that the domain of the function is (0,∞). First of all, let's…

Q: Find the length of the curve defined by the y-axis. over the interval <r< 1 about 2.r

A:

Q: Find the exact length of the curve. 36y2 = (x² – 4)3, 2 < x < 9,

A: Given:  36y2 = (x2 - 4)3 , 2≤x≤9,y &gt;= 0

Q: Find the exact length of the curve. x3 y = 1 < x < 2 %3D 4x

A: y=x33+14x  ,  1≤x≤2.

Q: Find the exact length of the curve. 1 y = -x° 4 x² -- In(x), 1<x< 4 | 2

A: Given curve, y=14x2-12lnx   ;  1≤x≤4

Q: Find the length of the curve y Inx at (2<x< 4)?

A:

Q: Find the length of the curve 3 y = x7 – 2 from x = 0 to X = 4.

A:

Q: Sketch the line tangent to f at the point corresponding to x = -1. Label it as T.

A: d) The tangent to the given function at x=-1 is as given in the following figure.

Q: Find the exact length of the curve. y = x2 - In(x), 1 < x < 4

A:

Q: . Evaluate the length of the curve, y = x/2, from x = 0 to x = 4. %3D

A: first step differentiate w.r.t to x

Q: find the slope of the curve at the point indicated. 19. у %3D 5x — Зх?, X =

A:

Q: Find the length of the curve of y=x³/2 from x=1 to x=4.

A:

Q: Find the length of the curve. y= x? + from x = 1 to x = 5

A: Please refer the attached image for complete solution. THANK YOU.

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: find the arclength of y= 9-x° between its x-intercepts

A: Find the x-intercept.

Q: I need to solve this question

A:

Q: Find the length of the curve 3y = (x² + 1) ? from x = 0 to x = 3.

A: Given:

Q: Find the length of the curve. 33) y-승. from x = 1 to x= 5 2x

A:

Q: Find the exact length of the curve. y = In(1 - x²), o sxs

A: Find dy/dx, then put it in the arc length formula.

Q: Find all asymptotes of the curve x2 + 3xy + 2y2 + 3x – 2y + 1 = 0 ?

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.