(=)- lim- sin +sin +..+sin В) -2 C) 0 E) - A) 2 D) 2

Q: 18 22 29 3. a. Segments of Chords Theorem b. Segments of Secants Theorem C. Segments of Secants and…

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Q: What is the Length of the arc of the circle r = sin θ that remains outside of the cardioid r = 1 —…

A: Arc lenght in polar curves: The formula to find the arc length is, Arc length=∫θ1θ2dxdθ2+dydθ2dθ…

Q: In AXYZ, the measure of ZZ=90°, YX = 97, XZ = 65, and ZY = 72. What ratio represents the tangent of…

A: Given: In △XYZ, m∠Z=90°YX=97XZ=65ZY=72 To find: What ratio represents the tangent of ∠Y?

Q: Use Green's Theorem to evaluate (sin r + y) dr + (cos y +a?) dy, where C is the square con- sisting…

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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 tangent of ZZ. 37 35 12 Y Write your answer as an integer or as a decima tan (Z) = Submit

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Q: Let f(x) = x³/2. Determine the length of the arc swept over x E la, b).

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Q: Find the arclength of y = 2x3/2 on the interval x is greater than or equal to 1 and less than or…

A: Equation of given curve is y=2x32 Differentiate with respect to x. dydx=232x32-1=3x

Q: Find the length of arc AB in terms of x.

A: Arc length is given by s=r.θwhere r = radius of the circle and  θ = central angle in radian

Q: Let CR denote the circle z = Rei (0 ≤ 0≤ 2π). Show that lim R→∞ CR 2-4 (2² + 1) (2³ — 5) dz = 0

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Q: Find the length of an arc of the curve y = In x from x = 1 to x = 2v2. !3! O 2.1206 2.1026 2.1602…

A: We know that arc length of the curve f(x) from a to b is defined as Arc Length = ∫ab1+f'x2dx Given:…

Q: Find the length of the catenary y = a cosh² from x = 0 and x = %3D X1.

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Q: Let θ be the angle between the line y = mx +b and the x-axis. Prove that         m = tan θ.

A: The slope of a line is the rate of change of the y-axis with respect to x. Formula for slope=riserun…

Q: Find the length of the arc of y=x^(3/2) between the points (1,1) and (4,8).

A: Find the length of the arc of y=x^(3/2) between the points (1,1) and (4,8)

Q: A- Using Simpson s Rule to estimate the area of the circle (r-4), c (1, 0) with (n=4). B- Prove…

A: The equation of a circle having center C(1,0) and radius r=4 is given by: x-12+(y-0)2=42…

Q: Find the length of are リ-Jx-2+ Sa'z) + Sin

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Q: Find the length of the arc of x²+y²=64 from x=-1 to x=-3, in the second quadrant.

A: Given curve: x2+y2=64

Q: A- Using Simpson s Rule to estimate the area of the circle (r-4), c (1, 0) with (n=4). B- Prove…

A: The equation of a circle having center C(1,0) and radius r=4 is given by: x-12+(y-0)2=42…

Q: The arc measure of UA is (3z +1).The measure of ADU is (22a - 16). What is the numerical value of…

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Q: 1. Line AB is tangent to circle O at A. If AB = 12 and OA = 5, find OB %3D B.

A: We have to find OB

Q: ind the length of the arc formed by x2 5y3 from point A to point B, where A = (0,0) and B = (25, 5).

A: Solution: The objective is to find the arc length

Q: Let f(x) = x3/2. Determine the length of the arc swept over r E (a, b).

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Q: In the figure on the right, xy and xz are tangents from an external point X. 1. Is XY congruent to…

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Q: Jose wants to explore the angles so he tried to push himself over the limit, he wants to answer the…

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

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Q: Find in terms of x and y if arctan(r + x²y) = ry

A: Given that         arctan(x+x2y) = xy We have to find dy/dx in terms of x and y.

Q: Give an example to justify that sin (A + B) is not equal to sin A + sin B. Limit A and B to special…

A: Special angles are those angles at which the values of the trigonometric ratios are known. For…

Q: lim yz? (2, y)(0,0) along y = 2x? %3D O does not exist 1/2 215

A: We have to find  limx,y→0,0yx2x4+y2 along y=2x2

Q: 9. Using the fact that lim | sin z e*dz = 0 , where C, = Re" , 0<oST, and that sin z has simple pole…

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Q: Show that the length of the perpendicular from the foot of the ordi- nate of any point on the…

A: We know the equation to the tangent at the point (x0, y0) is y-y0 = m(x-x0), where m is the slope.…

Q: ind the length of arc of the curve 6xy = x⁴ + 3, from the point where x = 1 to the point where x =…

A: Here given equation as 6xy=x4+3ory=16x3+3x Differentiate with respect to x…

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: This diagram shows a tangent TA with chord AB parallel to chord PQ.«

A: (a) To prove : ∆PAT is similar to ∆BAQWe can see that ABQP is a cyclic…

Q: GIVEN: In Figure 6.46, AB and AC are tangents to 00 from point A; B and C are points of tangency.…

A: Given, AB and AC are tangents to circle with center O from point A (external point). B and C are on…

Q: Find the length of the arc formed by x2 = 10y from point A to point B, where A (0,0) and B = (100,…

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Q: duct Theorem. 2. y= FH = 2.4 GI =

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Q: Find the length of one arch of the cycloid x= 5(t-sin(t)), y= 5(1-cos(t)).

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Q: a) In exercise 1.1, describe the erro statement of the tangent ratio.

A: Given : The statement, Figure :

Q: Express the circle specified by x = 2 cos(0) y = 1 + 2 sin(0) in Cartesian coordinates and find the…

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Q: Find the length of the catenary y = a cosh from x = 0 and x = a X1.

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Q: 5. Find the length of one arch of the cycloid x = sin and y = 1- cos 0

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

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Q: Given: AB and AC are B tangents to 00 from point A AABC is isosceles A Prove:

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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: Find the tangent of LC. C 2/7 7/2 В Write your answer in simplified, rationalized form. Do not…

A: In a right angled traingle value of tan theta can be obtained by dividing the length of opposite…

Q: Show that 8r units is the length, L, of one arch of the cycloid described parametrically by: x (0) =…

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Q: Prove that if 0 < x < 2r, then a circle of radius r has a chord of length x. (You can do this using…

A: According to given ,only 1st solved....Radius of circle = r

Q: In Oo, radius OD chord AB at point C. If OD = 5 and AB = 8, find OC. O 3.5 0 3 4 O O 39

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Q: 8 Find the distance from (1, 0) to (0, 1) along (a} a straight line (b) a quarter-circle (c) a…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.