Find the length of the curve r (t) = i + 6t°j + 2t°k, 0

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Q: A forest fire is found at midnight. It covers 1100 acres then. It is spreading at a rate of f(t) =…

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). ||r(t)||* r(t) = t'i + t°j

A: Here we have r(t)=t2i+t5j We have to find κ(t)=r'(t)×r''(t)r'(t)3 ..................................…

Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

A: Given x=et cost  , y=et sint , z=7 et

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Q: 4х Consider the function A(x)=2x+ for x > 3 Зx-1 (a) This function has one critical value larger…

A: We will start from critical points and follow upto inflection point

Q: x2- 2 (x+ 2)(x + 1)² x+2 (x + 1)2 x+2 (I + x) Option 1 Option 2 1 (x + 1)2 x+ 2 (x + 1)

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Q: Find the first partial derivatives with respect to x, y, and z. 7xz x+y

A: This question is related to differentiation, We will solve it using given information.

Q: 2r-4x2-x-3 dx x- 2r 3 In Ix+ 1 +3 ln|x-3| + C +1-3 ln|x-31+ C Option 1 Option 2 2 In |x + 1| - 3…

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Q: 13. Find the length of the curve y4 + 8 from y = 1 to y = 4. X = 4y2

A: To find the length of given curve.

Q: Consider the matrix -8 A = 13 21 1 4 -2 15, Where a;, represents the entries for A, for i= 1,2,3 and…

A: Given,        -8    0    5 A= 13    21  1         4    -2   15 a ij represents the entries for A,…

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Q: integrate dx/(x²+x)(x-1)²

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Q: Find all values of the angle 0 (in radians, with 0 s 0 < 2n) for which the matrix cos e -sin 0 A =…

A: The solution is given below

Q: 5. Use the Second Fundamental Theorem of Calculus to find F'(x). х 1 F(x) = S* dt.

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Q: Suppose a product's revenue function is given by R(g) is units sold. 5g? + 500g, where R(g) is in…

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Q: Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x2 b.…

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Q: find (2n +1)! = 120

A: Here we have to find the value of n.  2n+1!=120

Q: Evaluate the following sum: 3x + cos 2016 + cos (Write your answer in the simplest form, use…

A: The given sum,1+cosπ3+cos2π3+cos3π3+cos4π3+......+cos2016π3

Q: Find the moment of inertia with respect to x-axis of the area bounded by the parabola y = 4x and the…

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Q: :. Let x(t) = 2 sinh t , y(t) = cosh(t²) be a curve in the Oxy-plane, given in parametric form. (a)…

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Q: Evaluate the double integral over the rectangular region { 2(* sin(1) – y sin(z) dA; R= {(x,v) : 0 <…

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Q: Given the linear differential equation: y'' - y = cos(x) - 5sin(2x) Find the general solution…

A: Solving

Q: Find the moment of inertia of the area bounded by the curve x^2=8y, the line x=4 and the x-axis on…

A: Use moment of inertia concept

Q: sin x – 2+ csc x (c) sin x – 1 sin x CSc x sin x + 1 | 1 (d) cos(tan-l x) = V1+ x² 1+cos u (e) Using…

A: We have to answer following Questions.

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Q: Evaluate the line integral F. dr, vhere F(z, y) = -yi-rj and C is the curve y = v4-a from (2,0) to…

A: We have to find the line integral

Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it…

A: integration

Q: 3. y = In? (csc2x). Find y"

A: y=ln2(csc2x)

Q: rocket weighs 2500 tons at liftoff and burns fuel at a rate of 12 tons/minute. Express the rockets…

A: Given query is to find the expression for rocket weight and time.

Q: x2 dx (x+2)3 In |x + 2| + 4x+6 (*+2)a +C In |x + 2| – 4x+6 (x+2)a

A: To integrate.

Q: 4–6 Find the directional derivative of f at the given point in the direction indicated by the angle…

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x + 3 lim x--3 x + 27

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Q: Find the conservative vector field for the potential function by finding its gradie h(x, y, z) = 8x…

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Q: A large corporation with monopolistic control in the marketplace has its average daily costs, in…

A: Let's find.

Q: Approximate the point of intersection of the graphs of f and g. Then solve the equation f(x)=g(x)…

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

Q: Evaluate the integral. (5 – 2t + 3t2) dt |

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Q: Find div F and curl F if F(x, y, z) = 4y®z°i – 11a°z°j – 5xy'k. div F= curl F=

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Q: Find the general solution of the differential equation. 4dy + ydx = x²dy

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Q: Sing do Coso + Cose-2

A: LetI=∫sinθcos2θ+cosθ-2dθPut cosθ=uDifferentiate on both…

Q: Integral calculus, partial fraction decomposition

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Q: Question 2 Find the inverse Laplace transform of H(s) - (;+)-

A: H(s)=1s2-e-s1s2+2s+e-4s4s3+1s L-1{H(s)}=L-11s2-e-s1s2+2s+e-4s4s3+1s…

Q: In the year 2000, the population of a small city was 47,000. The population grows at a rate of r(t)…

A: For the following problem,

Q: *+ 2y = te-2t, y(1) = 0 2. Solve the IVP: dt

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Q: o<×くT ② Foのコ 2 [:

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Q: Find the moment of inertia with respect to x-axis of the area bounded by the parabola y = 4x %3D and…

A: Moment of inertia with respect to x-axis , Mx= ∫A y2 dA.

Q: Find the conservative vector field for the potential function by finding its gradient. 9 (r,y, 2) =…

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Q: find Fourier series on [0,2n] 0 0<x<7 (7) f(x) =. 1 T<x<2z

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Q: The depth of the water in a cylindrical tank 4 m in diameter is increasing at the rate of 0.7 m /…

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Q: Find the generating function for this when n=2, f(2)=1. n=3, f(3) = 6. n=4, f(4)= 25. n=5,…

A: Given :n=2, f(2)=1. n=3, f(3) = 6. n=4, f(4)= 25. n=5, f(5) = 125. n=6 f(6) = 750To find : The…