13. The figure shows a circular arc of length S and a chord of length d, both subtended by a central angle 0. Find lim (s/d) 0¬0+ d

Q: 1 1/2 Find the length of the arc cut from x = between the points ,1 and 13 -,4 3 N|3

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Q: Show that if 0 ≤ f' (x) ≤ 1 for all x, then the arc length of y = f (x) over [a, b] is at most √2(b…

A: The arc length increases with the value of f'(x) Means, if f'(x) increases then arc length will…

Q: lim y→0 \ In cos y O 2 O 1

A: We have, the given limit problem as limy→0y3lncosy On substituting y=0 directly into the given limit…

Q: If f(x) = 3x^2/3 − 10, find the arc length of the graph of f from the point A(8, 2) to B(27, 17).

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Q: Find the exact value of x. 45° 100 Lim (O [0] 7h 15 VI UC

A: The sine of an angle is the length of the side opposite the angle divided by the length of the…

Q: Find the arc length of y=sqrt(4-x^2) -2<=x<=2

A: The equation of the curve is given by y = 4-x2 : -2≤x≤2 To evaluate : The arc length.

Q: Find the length of the arc of the curve from point P to point Q. x2 = (y – 4)³, P(1, 5), Q(8, 8) %D

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Q: 4! find lim, B4,-2) S x approachesto I from postve direction.

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Q: Find the length of the arc x=(1/6)y³ + (1/2y) from [1,10] Answer:

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Q: Assume that the two points (x1 y1) and (x2.y2) lie on the graph of the straight line y = mx + b. Use…

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Q: Find the limit.

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Q: For B = – lim r² -1 6 sin z which one is B?

A: In this question we have the limit for B.

Q: 3. In the diagram, AC is a tangent to the circle with center O. What is the measure of x? Give…

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Q: Find the arc length of the graph of the function over the indicated interval.

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Q: If y = arctan x, then what restriction is placed on the value of y?

A: Consider the given function:  y=arctanxDomain of  arctanx:  −∞ &lt;x&lt;∞Range of arctanx:…

Q: Find the arc length of the graph by partitioning the x-axis. y = x3/2 + 2, from x = 3 to x= 5

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Q: Given lim (0,y)→(0,0) x4 + y? 1 and lim (2,22)→(0,0) x4 + y? 2 does lim (2,y)→(0,0) z1+y? exist?…

A: We have to find whether lim ( x, y ) tends to ( 0, 0 ) x2y / ( x4 + y2 ) exist or not .

Q: 1. If f(x) = 3x2/3 - 10, find the arc length of the graph from the point A(8,2) to B(27,17).

A: Note:  We'll answer the first question. Since the exact one hasn't mentioned. Please re-submit the…

Q: Find the exact arc length of the curve. x6 + 8 y = from x = 1 to x = 3. 16x2 Give the exact answer…

A: To Determine: find the exact arc length of the curve  Given: we have a function y=x6+816x2…

Q: Calculate the arc length of y = 15 – 14x over the interval [1,3]. (Use symbolic notation and…

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Q: blem 11.10. Find the arc-length from (-3, 4) counter-clockwise to 3) along the circle r2 + y? = 25.

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Q: From point P outside a cicle secant PCA and tangent PB are drawn. If PC is 4 and PB is 8, find AC.

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Q: Suppose that the temperature at a point (x, y) on a metal plate is T(x, y) = 4x² – 4xy+ y². An ant,…

A: Given the temperature is, Tx,y=4x2-4xy+y2. Since, the path of ant is  gx,y=x2+y2-16. By the method…

Q: - The area of a circle with radius r is The area of a sector whose measure of the arcs is a/an A of…

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Q: Find the arc length of the graph by partitioning the x-axis. y=(1-x2/3)3/2 , from x= 1/64 to x=1

A: Given function is y = y= 1-x2/33/2 from x= 1/64 to x=1 The arc length of a curve on the interval [a,…

Q: Evaluate the limit. sin? 3t lim t-0 O DNE O 0/0 O 3 9,

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Q: 1- cos(Vr² + y?) lim (x,y)→(0,0) • (a) Va2 + y?

A:

Q: 5. From the figure below, the small circle in the middle is tangent to each other of the three large…

A: Since radius of all three circles is 1, that means all three sides of a bigger triangle are same and…

Q: Find the arc length of the graph by partitioning the x-axis. y =2/3(x2 + 1)3/2, from x = 2 to x=7

A: The arc length of a curve y = f(x) over an interval [a, b] is given by the formula

Q: Find the arc length of the graph by partitioning the x-axis. y = x2/3 + 1, from x = 1 to x = 64

A: We first find dydx using the power rule. y=x23+1dydx=23x23-1dydx=23x-13

Q: In circle X, mZYXZ = 135° and the area of the shaded sector =T. Find the length of XY.

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Q: 2. The value of lim is (z.v)-(0,0) Vr² + y? (b) 1 a) 0 (c) 2 (d) does not exist

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Q: 37. Find the maximum area of a rectangle circumscribed around a rectangle of sides L and terms of…

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Q: In circle P with the measure of minor arc NQ= 120°, find mZN RQ. N Q R Answer: mZN RQ =

A: m(angle NRQ) = 60°  The detailed explanation is as follows below :

Q: 8. Let C be an arc of the circle [z| = R(R > 1) of angle t/3. Show that dz TT | + 3 \R3 - dz And…

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Q: find the entire length of one arc of the cycloid x=2A-2sinA, y= 2-2cosA.

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Q: The graph of fCx) below To evalvate tue following limits. Ao lim fex) 104 9. B. ling fCX) C.lim f(X)…

A: Given, graph of fxTo find: limx→2-fx limx→2fx limx→4fx limx→5fx limx→∞fx

Q: Determine the arc-length of the following: 1 3/2 x=y -y" for 1< y<9 3 1 а)

A: To find the arc length

Q: find the arc length of the graph f(x) = x5/10 + 1/6x3  over [2,5]

A: Let y = f(x) be a function.Then, the arc length formula for the graph of the function over [a,b] is,

Q: An arc PQ of a circle subtends a central angle 0 as in the figure. Let A(0) be the area between the…

A: Since PR is tangent so PR is perpendicular to OP where O is the center.  Thus, PR=r×tanθ2.…

Q: The shape of a hole pored by a drill is a cone surmounted by cylinder. If the cylinder be of height…

A: Consider the following figure. Given tanα=hr. We know that the volume of the cylinder is…

Q: Find the limits Sialve) , 3) - e* § + lim Sin(yt) Cos (3t) -1 も→D Sin? (4t) lim Yet ニ + lim Sin…

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Q: Find the arc length of the graph by partitioning the x-axis. y=1/3 (x2 +2)3/2 , from  x = 3 to x =…

A: Given: The function y=13x2+232  fromx=3 to x=4

Q: 1) (a) Evaluate |(2² – y°)dz +2rydy, along the circular C that is upper half-circle oriented…

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Q: Find the length of the arc of the parabola y sq = x from  ( 0, 0 )  to ( 1,1)

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Q: Q2 Start with a circle of radius 4 unite . Draw the second circle with radius 2 and the third one of…

A: Q2, Given that, One Circle with a radius of 4 units One circle with a radius of 2 units One circle…

Q: Use the formula for arc length to show that the length of a graph over [1, 4] cannot be less than 3.

A: Let a function be: Now for any given function y=f(x), arc length is given as:

Q: Find the arc length of the graph of the function over the indicated interval. 3/2 y = 3. y 20 15 10…

A: The length of arc y=f(x) between x=a and x=b is given by  L=∫ab1+dydx2dx

Q: s(2) is continuos if lim f(z) =f(z,)

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Q: Find the limits by rewriting the fractions first.

A: We have to find:

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.