||r(t) × r"(t)|| ||r'(t)||* Use the formula k(t) : to find k(t). r(t) = e"i+ ej K(t) :

Q: 8 f(x, y) = y/x, P(1,2), u = }(2i + 5 j) |(2i + /5 j)

A: To find the gradient at the given point and then rate of change for the given function.

Q: (b) Which of the following integrals is equal to –2+ ln 2? (a) 4 dx 4 (b) dx x² (c) / 4x dx x2 4 dx…

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Q: 7. 1 (x dy – y dx) = 0 %3D x² + y²

A: Here, the given DE is: 1x2+y2(x dy -y dx)=0...(1)

Q: 5 + 5(-5) + 5(-5)' +.. 4 Σ. 4 i= 1 8.

A:

Q: Find the divergence of the vector field F. F(x, y) = 5x2i + 5y²j

A: The given vector field is: F(x,y)=5x2i+5y2j Let, F(x,y)=F1i+F2j⇒F1=5x2, F2=5y2

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

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Q: Pu 6 • (2, 5) (4, –3) Graph of f 3. The graph of ƒ is shown above for 0 < x < 4, What is (A) –1 (B)…

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A: Here we have to find the particular solution of given differential equation.

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Q: Dest. 3. Supply Sources! 6. 3. 10 7. 20 3. 10 11 15 30 Demand 15. 17 28 Find the initial solution…

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Q: Use continuity to evaluate the limit. 16 + Vx lim 16 + x

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Q: on the interval Find the difference between the upper and lower estimates of the distance traveled…

A: Let's find.

Q: The study of integrals in calculus is motivated by the problem of calculatin (a) the slope of a…

A: Study of integrals in calculus is motivated by calculating the area of a region bounded by curves.

Q: 6. Find the indefinite integral. S 3x³ V3x4 + 7 dx (Use substitution method)

A: Solving the problem by finding the value of integration.

Q: A box with an open top has vertical sides, a square bottom, and a volume of 32 cubic meters. If the…

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Q: 3+ 12x4 – 7x +x³ a) lim 2л2 — За3 + х — 424 3x3 +x – 4x4* - -

A:

Q: (c) f(x) = sin? x [Hint: sin? r = l-cos 21] (a) f(r) = r arctan r b) f(x)=x²e- %3D

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Q: Find the derivative of the vector function r(t) = ta x (b+tc), where (5,-4, 1), b = {(-4, –3,1), and…

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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: The marginal cost for a company to produce q items is given by MC(q) = 0.004q - 0.9q + 615. The…

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Q: Find the curvature of the plane curve y = -t at the point t = 2. к(2) -

A: Given:y = -t4differentiating with respect to t, we get:            y' =     d(-t4)dt…

Q: 2r³ – 4x² – x – 3 dr x² – 2x – 3

A:

Q: 5. Find the general solution: 9y" + 12y' + 4y = 0.

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Q: TIIS que IS mat you are usng your calc necuy. Use a calculator to do this calculation. 10-15 3.9 x…

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5- 5 -5+ -5+

A: Given data÷

Q: Find the positive root of the equation x + 2x2 + 10x - 20 in the interval [1,2] using Regula Falsi…

A: Let, the given function be: f(x)=x3+2x2+10x-20 And, the formula of the method is:…

Q: tan(0)² cos(0) d0

A:

Q: i(x) = 2-0.8(x-43.79)

A: Given query is to find the derivative of the expression.

Q: Describe the graph of the equation. r= 5 cos t i - 18 sin 1 j +k O An ellipse in the planex = 1,…

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Q: lim (3x + 1) sin(2x) 4x2

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Q: (a) Use Green's Theorem to find the line integral over the simple, closed curve C : r(t) = (cos t,…

A: To use green's theorem to find the given line integral over the curve C

Q: In(1+x) -x cosx -1 1. lim x-+0 7- In(2x + 3) 3. lim x-00 In(5x -2)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: x+x-6 lim X-2 x-2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: For the straight line defined by the points (1,57) and (3, 87), determine the slope (m) and…

A: Solution is done in step 2

Q: 1. Given ä = (-2,–1,4),B = (5,2,3)and č = (-3,0,5) determine each of the followin a) ĉ b) |2ã – 7|…

A: As per our guidelines we are supposed to answer?️ only 3 question. Kindly repost other question as…

Q: on. 5x(8- х) dx x(8 - x) dx =

A:

Q: 2. Compute Ja F · ds for F c(t) = (t , In(1+ t²), e*) for 0 <t < 1 VV, where V(r, y, z) = 4x² In(1+…

A: Find your answer below

Q: Evaluate the line integral -ydx + xdy along the curve C C : y? = 15x from (15, 15) to (0, 0). NOTE:…

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Q: Find the 22 term of the arithmetic sequence whose common difference is d=4 and whose first term is…

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Q: e2x - e 2x 3. lim, 0 sinx

A: To evaluate the given limit.limx→0 e2x-e-2xsin x

Q: Find the exact value of: 1 + cot (Write your answer in the simplest form, use fractions whenever…

A: Trigonometric values cot2π6=32=3 sec2π4=22=2

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: The measure of an angle 337.5 degrees is equivalent to ra 15 A 4 15n 8 13п 8 13п D 4. B.

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Q: Consider f(x) = 6.9x3 + 9.1x2 - 4x + 7.7. Using the given function, approximate f(4) by making use…

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

A: To evaluate the value of  ∫-∞∞7x2+4x+8dx=7∫-∞∞7x2+4x+4+4dx=7∫-∞∞7(x+2)2+22dx

Q: dx 00 2 X х +4

A:

Q: x2 dx (x+2)3 In |x + 2| + 4x+6 4x+6 (ar+2)a +C In |x + 2| – (x+2)= Option 1 Option 2 희im lx + 2 +…

A: Given problem:-

Q: +y = e=* sin x

A:

Q: Find G'(x). In(9) G(x) = (4e- 7t + 1) dt G'(x) =

A: Given query is to find the derivative of the expression.

Q: The progress of a person on a long hike is shown in the graph. 9. D 8 - 7- 6 - B 2- 1- 5 7 8. Time…

A: The given graph is distance against time ,  where distance is marked on y-axis and time marked in…