Find the curvature and the radius of curvature at the stated point. r(t) = 5 cos(t)i+11 sin(t)j+4tk; t= NOTE: Enter the exact, simplified answers. V4961 41 V41 K = p =

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A: answer is in next step

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A: Given query is to find the area enclosed by the curve and x Axis.

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A: Topic:- geometry

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Q: Use Stokes' Theorem to evaluate curl F· ds. F(x, y, z) = ze'i + x cos(y)j + xz sin(y)k, S is the…

A: Stoke's theorem: The surface integral of the normal component of the curl of F is equal to the line…

Q: Čonsider the following equations. 3 f(x) .3 y = 0 X = -4 х3D —1

A: To find the area of the region bounded by the given curves.

Q: Consider the following functions. f(x) 3 Vx - 3 g(x) = x – 3 %3D Sketch the region bounded by the…

A: Let us first find the intersecting point. So,               x-33=x-3⇒x-3=x3-9x2+27x-27⇒x=2, x=3, x=4…

Q: Find V · (F × G), if F(x, y, z) = 2xi+j+14yk and G(x, y, z) = xi+ yj – zk. %3D - V · (F × G) = %3D

A: To solve the following problem

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Q: Evaluate the integral / (6x + 18y)dx + (12x – y)dy along the parabolic arc y = r from (0,0) to (1,…

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Q: Find V. (V x F), if F(x, y, z) = 3e"i+ 7xe"j – 3ek. V.(V × F)

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A: Explained below

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Q: 4. Evaluate lim (cos r)/**.

A: We know that limx→0f(x)g(x) is of the form 1∞ then limx→0f(x)g(x)=limx→0eg(x)f(x)-1

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Q: f(x) = (-3x³ + 4) 7, which of the following is f'(x)? f' (x) = 63x² (-3x° + 4)-8 - f' (x) = 63x(-3x…

A: Topic:- derivatives    Using  Derivatives of x^n = nx^(n-1)

Q: A company that produces cell phones has a cost function of C = 17x² – 444x + 18816, where C is the…

A: Given query is to find the number of units to minimize the cost.

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A: A 25‐year old woman burns 350-60t cal/hr while walking on her treadmill. Her caloric intake from…

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Q: 2 4 Find an equation of the normal line to the curve 3x¯y' – x°cos(ny) + 4x + 2 = 0 at the point…

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A: We need to find integral.

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A: Given,  f(x)= 1/sqrt(x-2)

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A: answer is in next step

Q: Use Green's Theorem to evaluate the line integral. y2 dx + xy dy C: boundary of the region lying…

A: Given problem:-

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Q: ||r(t) x r"(t)|| Use the formula k(t) to find k(t). r(t) = 8 cos(8t)i + 8 sin(8t)j + 5tk к(€)

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Q: Write the equation of the trigonometric graph. try sin x )+ 5 4. 2 31 57 37 2 -2 -3 -4 || 3. 1.

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Q: Evaluate (2x – y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 32)

A: This is a problem related to vector calculus. Based on green's theorem we will solve the integral.

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Q: Evaluate the line integral (2x + 4y)dx + (3x – 9y)dy along the curve C : æ = 2 cos t, y = 4 sin t (0…

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A: