Find the Length L of the curve R(t)= -2cos(4t)i + 2sin(4t) j + t k over the interval [2,6]. L =

Q: 7. Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Given a function of the curve, y=ax4+bx3+cx2+dx+e To find the coefficient a,b,c, and d such that the…

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

A: Given: x=et……1y=te-t……2 where t≥0   To find: Slope of line tangent at x=3

Q: On what interval is the curve t2 X. dt y% = Jo t2 + t +2 concave downward?

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Q: 2.) Find the acute angle between the given curves y² = 2x and 4x²+ 4y² +5y=0

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Q: 3) Find the exact length of the curve: x = y = In(1+t); 0<t<2.

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Q: Compute the length of the curve over the given interval. r(t) =〈2t, ln t,t^2〉, 1 ≤ t ≤ 4

A: it is known that the length of the curve can be calcualted by the integral formula…

Q: Find the length of the curve r(t) = (t2 /2)i +ln t j + t (2)1/2 k for 1<= t<=2

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Q: Find the equation of the tangent plane to z = ey + x + x2 + 11 at the point (5, 0, 42).

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Q: 18. The length of the curve y = r* from r = 0 to r = 2 is | V1+2® VItz® dz B. | V1+3x2 dx A. C. D.…

A: Question 18 is solved. Solving more questions are against the policy of bartalby. In question 18 ,…

Q: (B) The length of the curve r(t)=(1+1)i+(1-1j+r/2k from the point t=- to the point r= is 2. -IN

A: The length of the curve means the arc of the length of the curve . The arc of the length of a curve…

Q: Consider the curve in the xy-plane repre- sented by = e' and y = The slope of the line tangent to…

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Q: Find the length of the curve y = Vcos 2t dt from x = 0 to x = T/4.

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Q: Find the exact length of the curve. y= In{1 – x²), o s 1. 0 sxs! 7. I Ju =

A: We will find the exact length of the curve as shown below

Q: (B) The length of the curve r(t)=(1+1i+(1-nj+rV2k from the point t= to the point t=; is 2. - 112

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Q: Find the maximum height above the xy-plane of a point on r(t) = (e1 , sint, t(4 - t))

A: Maximum height above the x-y plane will be the maximum value of z .So we will take z parameter of…

Q: Find the distance between the point (-2m, 0, -m) and the tangent line of the curve ū(t)= (me* – }i--…

A: Given: u-(t)=(met2-t)2i-4mt+1j+t-mt2+1k at t=0 First we will find tangent line of the curve…

Q: Express the curve by an equation in x and y given x(t) = e' and y(t) = 7 – e2'. a) O-x2 + y = 7, x 2…

A: simplify the equation and choose correct equation.

Q: The curves C,:x=t, y=t, z=t, t20 and C,: x= sint, y 1+cost, z=1, 120 have intersection at the point…

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Q: 3. Find the length of the curve r = e® for 0ses 2n.

A: Given polar curv er=eθ   ; 0≤θ≤2π

Q: (ii) Find the length of the curve y = E* from x = 0 to x = 2. %3D

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Q: (6) Find the points on the curve 5x2 + 6xy + 5y² = 9 which are nearest to and farthest from the…

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Q: For the curve y = f(x) = x², 0 ≤ x ≤ 2, its length is 2 L = 1+ dy dx dx =

A: Given curve y=f(x)=x2,0≤x≤2 The objective is to find the length of the curve.

Q: compute the length of the curve over the given interval.  r(t) = (2t2 + 1, 2t2 − 1, t3), 0 ≤ t ≤ 2

A: Length of a curve is also like computing distance between two points but with the restriction that…

Q: On what interval is the curve y = 0, v- [ t2 dt t2 +t + 2 concave downward?

A: NOTE: Refresh your page if you can't see any equations. . to find the inflection point, first, we…

Q: Given F(x, y) = [arcot(/K)-(secx)* - 2y]i+ 3x-es 2021 evy and the curve C=C,UC,UC, as shown in the…

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Q: ) Find the gavea d the rgion enclased by the line x-In3 and the curves y= ex and y=ex

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Q: FInd the length of the curve of r(t)= on the interval [0, 3]

A: The given curve of r(t)=t3,t, 7 for the interval [0, 3]. Formula used : The curve length is given by…

Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = 4

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Q: Find the equation of the tangent plane to z = ey + x + x² + 7 at the point (5, 0, 38). = Z |

A: To find the equation of tangent plane to z=ey+x+x2+7  at the point 5,0,38In general the equation of…

Q: Find the Giniindex for the lorenz curve L (X)= 0.3X + O=7X 11

A: Given the Lorenz curve Lx=0.3x2+0.7x. Find the Gini index of the Lorenz curve.

Q: C is the curve y = e® from (2, e²) to (0,1) and F = (x², -y), compute ſ, F-dr.

A: Given that, C is the curve y=ex from 2,e2 to 0,1 and F=x2,-y Then, F=x2,-y=x2,-ex So, F→=x2i^-exj^

Q: Find the length of the curve r(t) = (√2t)i + (√2t)j + (1 - t2)k from (0, 0, 1) to (√2, √2, 0)

A: given, r(t)=(2t)i +2tj+1-t2kwe have to find the length of the  given curve from (0,0,1) to 2,2,0

Q: Let C be any curve.

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Q: Find the equation of the tangent plane to z = e9 +x + x³ + 6 at the point (3, 0, 253).

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Q: Determines the length of the curve in the indicated interval x = 3 sin t+ 3t, y = 3cos t, 0stsm O 12…

A: Given curve is x=3sint+3t and y=3cost, 0≤t≤π. We have to determine the length of the curve on the…

Q: 2. Find for the curve dx x²y3 – 2xy = 6x² + 2y³ + 1 -

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Q: Compute the length of the curve r r(t) = (2t, In t, t²) over the interval 1 < t < 3 L =

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find an equation for the tangent plane to the graph of f(x, y) V3+ r2 – 3y2 at the point P(2, 1,…

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Q: Find the orthogonal trajectories of the given family of curves. 1. y = c (sec x + tan x )

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Q: Find the length of the curve r(t) = 6t°i – 2t³j – 3t³k from t = 1 to t = 2.

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Q: Find the length L of the curve R(t) = 4ť²i + t° j+ 4k over the interval [3, 6]. L

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Q: On what interval is the curve t2 dt t2 +t+2 y = concave downward?

A: The given curve is: y=∫0xt2t2+t+2dt Using fundamental theorem of Calculus says: ddx∫axf(t)dt=f(x)…

Q: 3. Find the equation of the plane tangent to the graph of f (x, y) = 3x + 4y – xy at the point (1,…

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Q: EX Find the point the curve y=x3+x²-l where the tamjent on is parallel to the X-oaxis

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.