Sketch the region R of integration and switch the order of integration. P(x, y) dy dx F(x, y) dy dx = f(x, y) dx dy

Q: If x + 1 f(x) then find the global maximum of on the interval [1, c0) Write DNE if there is no…

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Q: Find V x (V x F) if F(x, y, z) = 4.xyj+ xyz k. V x (V × F) =

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Q: Apply the Ratio Test to each series to determine whether the series converges, or state that the…

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Q: he curvature and the radius of curvature at the stated point. r(t) = 3 cos(t)i + 4 sin(t)j + tk; t 2…

A: Please refer to the image below

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

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

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: ||r(t) × r"(t)|| Use the formula k(t) : to find «(t). %3D r(t) = e"i+e-tj K(t):

A: K(t)=?

Q: Find V· (V × F), if F(x, y, z) = e*²i+3xe'j – 7e*k. V . (V × F) = x z evz 三

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Q: work shoWN. 1. Let v and w denote nonzero vectors. Show that the vector v- aw is orthogonal to w V.…

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Q: Evaluate the line integral (6x + 8y)dx + (3x – 3y)dy along the curve C: x = 4 cos t, y = 8 sint…

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Q: Find V · (F × G), if F(x,y, z) = 3xi+j+7yk and G(x, y, z) = xi+ yj – zk. V• (F × G) =

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Q: 20. Evaluate dædy by changing the limits of integration appropriately. e y/2

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Q: Evaluate the triple integral of f(x, y, z) z(x2 + y? + z2)-3/2 over the part of the ball x2 + y² +…

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Q: Find div F and curl F if F(x,y, z) = xzºi+ 5y°x²j+ 5z?yk.

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Q: Find the 4** x³ dx А. + c 4 In 4 В. + c 4 In 4 С. + c 3 In 3 D. 24 2 In 2

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Q: Find div F and curl F if F(x, y, z) = 3e*"i – cos yj+ 7sin? z k. %3D div F= curl F=

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

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

Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

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Q: An unknown function's derivative is h'(x) = 3x-2 - 6. Using your understanding of the derivative…

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Q: (6x- y+3)dx+(3y'-x-2)dy 6) Integration Factor Method rahee

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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,…

A: Given :f=x3-y3

Q: 1. Sketch a single graph of a function f(x) which satisfies all of the following the limits and…

A: The function satisfies,f-3=1, limx→-4f(x)=-1, limx→2-f(x)=-∞, limx→2+f(x)=∞, f'(4)=0f(2)=2,…

Q: Solve the system of differential equations. [ 3 x' 0 - 4. x1(0) = – 12, x2(0) = – 10 - æ1(t) = %3D…

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Q: Let f(x) = 9x* + xx² + e2*. Compute f©(x). (Use symbolic notation and fractions where needed.) f9(x)…

A: Compute 5th derivative of f(x)

Q: Use a double integral to find the volume of the indicated solid. 4아 2 30 z = 25 - xy 20 10 3. 2 y=x…

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Q: (2) Prove that for any integer L () NTX / sin? dx = L. L -L

A: ∫ cos(ax) dx = 1a sin(ax) +C

Q: Find the derivatives of the following functions: Inx i) y = sin3x? ii) y = e2*cosx iii) y = 3r+5

A: i)y= sin 3x2y' =ddx sin 3x2y' =cos 3x2  ddx(3x2)y'=cos 3x2 (3)(2x2-1)y'=(6x) cos 3x2

Q: 1. Do the integration by substitution for the following integral and find the value of definite…

A: We have to find the given integral value.

Q: Describe the graph of the equation. r = 15 sin 5t i + 15 cos 51 j O Itis a circle of radius 15 in…

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Q: S%3200000 e° find the growth rate of S.

A: Given query is to find the growth rate.

Q: 14th term of the following geomnetric sequence. Find the 1. 2, 4, 8, 0. 昌 唱

A: Use geometric series concept

Q: Find an equation in cylindrical coordinates for the equation given in rectangular coordinates. (b)…

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Q: sin° xcos xdx x cos'

A: We will use substitution method to solve this definite integral.

Q: A. Sketch the figure for analysis. Shade the needed region and draw a representative vertical or…

A: Here, the region is bounded by the curves: x=4, y2=x

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: Evaluate the line integral -ydx + xdy along the curve C : y? = 24x from (24, 24) to (0,0). NOTE:…

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Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: 4 3…

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Q: Find V x (V × F) if F(x, y, z) = 4xyj+ 9xyz k. V x (V × F)

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Q: For the given position vectors r(t), compute the (tangent) velocity vector r'(t) for the given value…

A: Find derivative of position vector then we get velocity vector then put the given value

Q: Find curl (5z i + 6x j + 2y k). curl (5z i + 6x j+ 2y k) = ( i )i + ( i )j + ( i )k Save for Later

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Q: dy 2 + y = 0, y(0) = -3 dt

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 5 Sine cose do 1. Sine+ 3sine - 4

A: Indefinite integral

Q: Find the area inside the circle r = = cos 0, but outside the circle r = 1/2. Sketch the graphs first

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Q: 8. 1) Use the Integral Test to determine whether the series is convergent or dive n' +1 n=1 Please…

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Q: 14. Use the curve sketching procedure to analyze the function. a. y-x'+x²-20x а. 1+x? b. y=- 1-x?

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Q: Use the graph of the function f to decide whether the value of the given quantity exists. (If an…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: Find the global minimum of the function f(x)=2x^3+3x^2–12x+4 on the interval [-4,2].

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Q: The position vector r describes the path cof an object moving in space. Position Vector Time r(t) -…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. p…

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Q: 2Tan 'x - x 9. lim,0 'x0 2x – Sin 'x

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