Use the Trapezium Rule with four strips to estimate the value of: dz. (In z)² Give your answer correct to 5 decimal places.

Q: Use the trapezoidal rule with n = 4 to approximate cos(x) dx finel

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Q: Find Equatien of the tavgnt lin tu th cuve at tk giver pointe y= sec X ,

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Q: Use these 3 methods to approximate , ex dx, n = 8 a. Trapezoid Rule b. Midpoint Rule c. Simpson's…

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Q: Find an arc length parametrization of the line y = 2x – 6 %3D |

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Q: e = 11rad %3D r= 2/5 Radius: Central angle: Length of the arc:

A: Consider

Q: Use the arc length formula to find the length of the linex = t, y = t, for 0 ≤ t ≤ 1.

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Q: What does the arc length formula give for the length of the line y = x between x = 0 and x = a,…

A: line y = x between x = 0 and x = a

Q: 2 cos(2x) dx, n = 4 J1

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Q: The work done W,to stretch a spring from its natural length to an extension of 6 meters Is given 6.…

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Q: Find the measure of arc RQT. U 44° T V R 25 S

A: We have to find the angle

Q: Find the arc length of the curve y 1 on the interval [1, 2]. %3D 4x2

A: Given:    y = x4/8 + 1/4x2   Interval : [ 1 , 2 ]

Q: Find the length of the equiangular spiral r = e° for 0 < 0 < . L =

A: Find the derivative r' with respect to θ. r=eθ for 0≤θ≤15π10a=0 , b=15π10r'=ddθeθ=eθ

Q: 11. Evaluate 2 dA, where D is the shaded part inside the semicircle of radius 2 in Figure 26. 2…

A: To Find:  D is the shaded part inside the semicircle of radius 2 From the figure, the restrictions…

Q: 4. By revolving the semicircle x = cost, y = sint (0 <t< ) about the x-axis, show that the surface…

A: Equation of semicircle with radius r is x=rcost, y=rsint We know the formula for surface area for…

Q: 2 b.f V1 + x³ dx

A: The given integral is√(1+x3) limit from 1 to 2.

Q: x = r², y = (0 <1 < 1)

A: For x=x(t), y=y(t), a≤t≤b Arc length formula is L=∫abdxdt2+dydt2 dt

Q: Find the surface area of a sphere of radius r using the formula of arc length with respect to x.

A: The objective is to find the surface area of a sphere of radius r using the formula of arc length…

Q: The center of gravity of a quadrant of a circle lies along its central radius (r) at a distance of…

A: ANSWER: TRUE

Q: Evaluate A = Se-* dx þy trapezoidal rule with n= 10. Work for 6 digit

A: Mathematically the derivative of a function is defined as f'(x)=limh→0f(x+h)-f(x)h. According to the…

Q: Find the arclength of r(t)= on the interval from t equals zero tot equals 2 times pi.

A: Given:  r(t)=&lt;5cot(t), 3 sin(t), 4 sin(t)&gt;To find:  Arc length form t=0 to t=2π

Q: Y 59° Z. 138°

A: See attached file for a step by step explanation to find required arc XY.

Q: Find the Arc Length of y= 3ln(x) - ((x2)/24)) on [1,6]

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Q: 4. Given YZ tangent to oJ at point Y and m<WYZ = 104, %3D what is the measure of WXY?

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Q: Find the length of the arc of the curve y = In x over the interval: [1, 9| . Round the answer to…

A: This is a question related to derivative of the function. Based on the general formula we will find…

Q: Approximate using the Trapezoidal rule with n = 4 subinte Round to 4 decimal places. sin r dr

A: See the details solution in below

Q: Find an arc length parametrization of the line y = 8x. r:(s) = %3D

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Q: Find the length of the curve y = = cosh(x), 0 < x < 1. Arc length =

A: Arc length of a curve y=f(x) on [a,b] is given by, L=∫ab1+y'2dx ddxsinh(x)=cosh(x)…

Q: The lateral (side) surface area of a cone of height h and base radius r should be Ar v? +h?, the…

A: Consider the provided question, Given the line segment, y=rhx,  0⩽x⩽h Differentiate both side of…

Q: Find the mZR in trapezoid QRST where QT||RS below.

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Q: Find the arc length of curve represented by X=cost+tsint   , y=sint-tcost               (0≤t≤π)

A: We know that: if parametric equation of a curve x=f(t) and y=g(t) is bounded by the region a≤t≤b,…

Q: Approximate the arc length to three decimal places given: y = In(cos x) , [0,÷]

A: Given curve is Differentiating with respect to x, we get

Q: Use Simpson’s Rule with n = 10 to approximate the length of arc of r(t) = t i + t2j + t3k from the…

A: Given,

Q: Find the arc length of y (x + 7)3 + (x + 7)-1 for 1 < x < 2. (Give your answer to three decimal…

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Q: Find the point On the curve R(1) = 5sint i+5cost j+12t at adistance (267) units along the curve from…

A: R(t)= 5sint i + 5 cost j + 12t k V=dR/dt =5sint i + 5 cost j + 12t k V= |v|= [(5cost)2 + (-5sint)2 +…

Q: s being pumped into a spherical ballo nge of the radius when the radius reac

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Q: (a) Obtain the equation of the tangent plane and the condition for tangency to the conicoid Ar? +…

A: Conicoid given is- Ax2+By2+cz2=1 at the point (α,β,γ) We have to obtain the equation of the tangent…

Q: Calculate the arc length of y = G(18x)3/2 – (18x)2) over the interval [2, 8]. (Give your answer to…

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Q: Find the mibimal distance between the foint Cl,4) to the linz Yeメtl. dっしくーメュ+(-

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Q: Find the angle of tilt θ with the horizontal so that the contact force at B will be equal to 0.76…

A: Draw the free body diagram of the block.

Q: B- Use the Trapezoidal rule with n=2 to estimate dx, to find the absolute relative true error |E,?

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Q: Compare the Trapezoidal rule and Simpson's rule app 4 x sin x dx

A: Given: An integral ∫0π4xsinx dx. To find: Bound for the error using the formula for each rule and…

Q: What does the arc length formula give for the lengthof the line r(t) = ⟨2t, t, -2t⟩, for 0 ≤ t ≤ 3?

A: Given:          r(t)=⟨2t,t,−2t⟩  for 0≤t≤3.

Q: Find the arc length of the portion of the curve y = 9x with 0 Sr<1. %3D Round your answer to four…

A: Given: y=9x20≤x≤1

Q: A figure on d coordinate plane is dilated using the rule (x, y).

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Q: Find the arc length of y = 7r +1 over the interval [0, 2]

A: y = 7r + 1 arc length=∫02 1+(dy/dr)2dr dy/dr = 7' arc length=∫02 1+(7)2dr arc length=∫02 50dr arc…

Q: The lateral (side) surface area of a cone of height h and base radius r should be pai rsqrt(r2 +…

A: Obtain the lateral surface area as follows.

Q: A flat, very thin table has a circular hole with radius 1 and a circular hole with radius 2. The…

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Q: Find an arc length parametrization of the line y = 8x + 7. r;(s) II

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Q: By revolving the semicircle x = r cos t, y = r sin t. (0 ≤ t ≤ π) about the x-axis, show that the…

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.