7-18 - Find the exact length of the curve. 7. y = 1 + 6x³/², 0 < x < 1

Q: 2 3/2 between x = 0 and x = 1 is 3 %3D The length of the curve y =

A: We will find out the length of curve.

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

A:

Q: |-*^= 39. What is the length of the curve y = √x- between x = 0 and x = 2?

A:

Q: 3n Q10:- Show that the point (2,) lies on the curve r=2sin 20. 4

A: 10) Given curve is r=2sin2θ show that (2,3π4) is a point lies on the curve

Q: 28. The line tangent to the graph of g at the point (x, y) inter- sects the x-axis at the point…

A:

Q: 66) The curve y = ax2. point (2, 28) and is tangent to the line y 2x at the origin. Find a, b, and…

A: We know that,The slope of a curve y = f(x) is given by m, where m is

Q: 3Keth curve ,Orienlation, regtangular equation. X = t-1 1-7

A: The given parametric equation is as follows. x=t-1 y=tt-1 For the value of y to be defined, its…

Q: Calculate the length of the curve defined by x =- Vy(y-3)on the interval 1 < y < 9.

A: Solution:  Consider the given curve:  x = 13y(y−3) on the interval 1≤y≤9 Since we know that the arc…

Q: Y = 3x 5 – 5x3 + 4 Y = (2x – 1)² (x² - 9) %3D

A: y=3x5-5x3+4y=(2x-1)2(x2-9)

Q: 10. Find the length of the curve y = x/2 + 8 on the interval [0, 2]

A:

Q: Find the points that touch the x axis of curve v = u2 + pu (n+1). Where n = 744. Also find the…

A:

Q: curve at the given point. 64. x² + 4xy + y² = 13, (2, 1) %3D

A: I have differentiate and find slope of normal and tangent line Then use formula for equation of…

Q: 6. Find the member of the curve whose slope at any point is √y and passes through the point (2, 1)

A:

Q: Find the exact length of the curve. y = 2/3(1 + x2)3⁄2,      0 ≤ x ≤ 4

A:

Q: 24. Consider the curve defined by the equation below and a point (2, 1) on the curve. What is the of…

A: Given query is to find the slope of the tangent line at point (2,1).

Q: 11. Find the length of the curve y = 2x3/2 x!/2 from x = 1 to x = 4. 2

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2 The equation of the tangent line to the graph y at the point (-1,2) is given by O a) y = 6x + 8. O…

A:

Q: 4. Find the exact length of the curve. 36y2=(x²-4)3,2≤x≤3.y≥1

A:

Q: 2. Find the values of a and b for the curve cos(Ty) 1 by² + ax² – x + 1 %3D if the point (1, 2) is…

A:

Q: 3 Q1. Q1. Find the length of the of the curve y = x2 X2 - from x 0 to x 3.

A:

Q: + 6) 2. Find the points where the tangent is parallel to x-axis, y =(x - 3a

A:

Q: Find the length of the curve. 30) x = 3 ty 3/2 - y 1/2 from x = 16 to x = 25

A:

Q: 7. Find the length of the curve y = x/4 on the interval [0,8] %3D

A:

Q: 3 Find the x-coordinates of all points on the curve y = (-x² + 8x – 7)° with a horizontal tangent…

A:

Q: Calculate the length of the curve defined by Vy(y-3)on the interval 1 < y < 9. x =-

A: Solution: Consider the given curve: x = 13yy-3 on the interval 1≤y≤9 Since we know that the arc…

Q: 3 Find the length of the curve y = x² – 2 from x = 0 to x = 4.

A: Given curve is y=x32-2 Upon differentiating we get dydx=32x12 We know that length of…

Q: Can you help me step by step?

A: Given equation of curve is y=ax2+bx+c which passes through (1, 3) so point (1, 3) will satisfy the…

Q: ii) Prove that the straight line y = x is the curve giving the shortest distance between the points…

A:

Q: Find the exact length of the curve over the given interval. 4 3/2 X= 3 1sys4

A: Given curve is x=43y32, 1≤y≤4

Q: 3- Find the length of the curves in Exercises 1-4. X = (y3/2/3) - y¹/2 from y = 1 to y = 9

A:

Q: 7-12 Find the exact length of the curve. 9. x = y/2, 0 <y<1

A: Length of curve is given by ∫y = ay = b1 + dxdy2dy

Q: 5. Find the length of the curve = = = (1 ²+2) X=- 3 9 0≤ y ≤ 4

A:

Q: 5 Find the equation of line tangent the circle x+y = 25 at point (3, -4). .2 %3D

A:

Q: Nem 7. (1 point) To find the length of the curve defined by from the point (0,0) to the point…

A: Answer and explanation is given below

Q: 3 where do the curve of y = cosx and y = x³ -1 intersect?

A:

Q: Find the length of the curve Y = 4x^3/2 from x = 0 to x = 5/16

A:

Q: 5. Find the length of the curve x = +22 from y =0 to y=3.

A:

Q: 8) Find the slope of the tangent line to the graph at the given point. (x? - y)? = 4x²y - 3x - y,…

A: The slope of a tangent line to a curve is the differentiation of curve with respect to x at a given…

Q: 25) Find the point on the curve y = Inx that is closest to the point (2, 3) with two digits accuracy…

A: So the point (2.731,1.0046) are closest to the curve y = ln (x)

Q: 13. BONUS: Find the coordinates of all points on the graph of y=1-x at which the tangent line passes…

A:

Q: The length of the curve defined by x =÷(y² + 2)E, y E [0,3] %3D

A: Arc length=∫ab1+dxdy2dy

Q: Discuss the properties of the curve (w/ solution) and sketch fully: 1+lnx y =

A:

Q: Consider the the curve y =(6x + 5)V6x + 5 from x =5 to x 11 a) Find the initial and terminal points:…

A: Consider the curve y=6x+56x+5 from x=5 to x=11.a To find the initial and terminal points.b To find…

Q: 10. Find the length of the curve y = x/2 + 8 on the interval (0, 2]

A:

Q: A curve for which y" = x passes through the point (1, –1) with a slope of. Find the y-value of at x…

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

Q: d the exact length of the curve. =√y (y - 3), (y - 3), 4 ≤ y ≤ 16

A:

Q: roblem 5. Find the equation for the line tangent to the curve y√ = 3x√√y - 10 at x =

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.