||r'(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). 3 r(t) = t'i + tºj %3| K(t) =

Q: I need help with this question (Not honor class) (Not grading)

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Q: Evaluate the iterated integral. 4ze dy dx dz

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

A: Here, to maximize the function f(x,y,z)=xyz using the constraint g(x,y,z)=x+y+z-6=0...(1)

Q: Find the length of the curve, L. y? = 64 (x + 5)* , 0 0

A: The solution is given in the next step.

Q: Find div F and curl F if F(x, y, z) = 13y*z'i – 11a'2®j – 5xy*k. div F= curl F=

A: We can solve as follows

Q: Express the iterated integral as an equivalent integral with the order of integration reversed. r36…

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Q: Sketch the region enclosed by the curves and find its area. y = cos8x, y = 0, x = π/16, x = π/8

A: Given: y = cos8x, y = 0, x = π/16, x = π/8

Q: Evaluate the integral by choosing a convenient order of integration: x cos(xy) cos' (Tx) dA; R 0, x…

A: Given

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Q: +4

A: To check the convergence of the given improper integral:∫-∞2dxx2+4

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Q: Question 8 Find the area of the region(s) enclosed by the curve y = |2x - 6|, the x-axis, and the…

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Q: Find the approximate area under the curve of f (x) =x+1 from x = 0 to x = 2, using 4 left-endpoint…

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Q: Using the substitution u = sin (x), or otherwise, find the exact value of %3D J sin° (x) cos (x) dx.…

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Q: (d) Select the correct choice below and fill in the answer box within the choice. O A. lim f(x) = X…

A: Let's find.

Q: .

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Q: Find curl (9z i + 10x j + 5y k). curl (9z i + 10x j + 5y k) = ( i )i + ( i j + ( i

A: Curl

Q: Find the exact arc length of the curve over the stated interval. 1 1 + from y = 1 to y = 3 x = NOTE:…

A: Aec length of the given curveL=∫131+dxdy2dy    Considerx=16y3+12y-1thendxdy=(16×3y2)+-12y2…

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A: Given that: The weight of the lunar module on surface of the earth, We=12 metric-tons The height to…

Q: 34 Count lim (1+x) F b) lim (1-x)* メ→0 The limit in (a) determines e. What special number does the…

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Q: Find the area of the region that is enclosed by the cardiod r = 14+ 14 sin 0. NOTE: Enter the exact…

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Q: 1-sine Evaluate the iterated integrals J. J. r2 cose dr de A) 1 B 2 c) o D) 3

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Q: Use double integration to find the volume of the solid bounded by the paraboloid Z = 9x + y, below…

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Q: Find the directional derivative of the function at P in the direction of v. g(x, y) = V x2 + y2,…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x3 - y3, P(4,…

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Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: Find the area of the region enclosed by the curves y = x² and y 4.x by integrating with respect to…

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Q: +1++4+ +7++10 written in sigma notation is equal to The sum 3k-5 A k=1 3k - 4 B k=1 3k-2 k=1 3k-1…

A: Let's find.

Q: Find the area of the region bounded by the equations y= x and Y3D6X-x². Note: theses are conics.

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Q: Skatch the curve in polar coordinates. r=I+ 3sino 2 -6 -4 -4

A: Given curve r= 1+ 3sin( theta)

Q: X+2 At what points is the function y = continuous? 2 X- 9x + 14 ... Describe the set of x-values…

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Q: 4 y=V4x- 2/2x

A: Topic = Derivative

Q: Evaluate the limit using L'Hospital's rule: Lim0+1 In(x+1) 2xe"

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Q: Evaluate the line integral / (x +8y)dx + (5x – 4y)dy along the - curve C : x = 8 cos t, y = 16 sin t…

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Q: Use a double integral to find the volume under the plane z = 32x + y and over the rectangle R = {(x,…

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Q: 1. Find the equation of the tangent line to the curve x = e', y = et att = 1. 2. Find all values of…

A: tangent property

Q: Find the distance of the centerof gravity of the area on the first quadrant region bounded by the…

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Q: Find the approximate area under the curve of f (x) =cos (5) from x = 0 to x = TT, using 4…

A: Here, the interval [0,π] is divided into 4 intervals of the length of each interval is ∆x=π-04=π4.…

Q: Use a double integral to find the volume under the plane z = 22x + yand over the rectangle R = {(x,…

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Q: rl+ 4sino

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Q: A torus is formed by revolving the region bounded by the circle x? + y? = 49 about the line x = 8…

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Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A: Given

Q: ind lim f(x) for the given piecewise function. x-4 2х + 5 if x 4 E the limit does not exist, enter…

A: Topic  = Limits

Q: The graph of y=- 50co has a horizontal shift of A units with respect to the graph of y= - 50cos(x).

A: This question is related to Trigonometric functions, we will solve it using given information.

Q: Evaluate JJ xy dA, where R is the region in (1, 3) (5, 3) (2, 1) (4, 1)

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

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Q: Edit Evaluate the line integral -ydx + xdy along the curve C : y = 21x from (21, 21) to (0,0). NOTE:…

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy -162 -108

A: ∫02∫-162y2∫-108zyz dx dz dy∫-108zyz dx=(xyz)-108z…

Q: Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = t = 0 T(0) = N(0) =

A: Unit tangent and normal vector

Q: Determine the area of the region bounded by y=2x^2+10 and y = 4x+16

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