Find V x (V x F) if F(x, y, z) = 9xyj+ 5xyz k. V × (V × F) :

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A: we use the basic formula ∫xn dx =xn+1n+1+C    ; n≠-1

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A: First draw the graph Uasing limits and the check the countinity of this function

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

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A: Given query is to find the equation of the tangent at x = 1.

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A: Solution is given below:

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A: This is a problem related to integration. Based on the integral formula for area calculating we will…

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Q: y" - 2у/ + у 3 tet + 4, y(0) — 1, у (0) — 1 || %3D

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Q: Find V. (V × F) if F(x, y, z) = 10 sin ci + 9 cos(2.x – 3y)j + 9zk. V·(V × F) =

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Q: Take

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Q: Find V · (V × F), if F(x, y, z) = 5e²i+ 5xe®j– 7ev²k. %3D V ·(V × F) =

A: We know divergence of curl of any vector v is always zero.

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A: This is 0/0 form so use L hospital rule and Solve.

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Q: r3 5x-2 5.) . V5x+1 xp!

A: This is a problem of integration. Based on the general formula and concept we will answer the…

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

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A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

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Q: #1 Evaluate F• dr. F(x, у) — хі + уј C: r(t) = (9t + 2)i + tj, 0sts1

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A: Rate

Q: d 5x+3 4. dx 7x+2

A: As we know that; The Power law: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2 And c·f'=c·f' ; where…

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A: According to rules.. I  need to solve 1st question

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A: Given query is to find the the integral for the area of shaded region.

Q: Find curl (5z i+ 6x j+ 8y k). curl (5z i+ 6x j+ 8y k) = ( )i + (i Oj + ( i Ok

A: Given that,    curl5z i+6x j+8y k

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A: We can solve this as follows:

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

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Q: II. Find the Inverse Laplace of the following 1 a. s² +6s+25 s2 b. (s-1)3 7 C. s4 8 - - - s3 s2

A: According to bartleby guidelines when student post multiple subpart questions then expert must have…

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A: We can solve this as follows:

Q: cx2 + 8x if x < 3 Let f(x) = 1 x3- cx if x 2 3. For what value of the constant c is the function f…

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Q: हम - (2) / हर्े 3

A: We can solve the given problem as follows:

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

A: As we know that; The Green's theorem; ∫CPdx+Qdy=∫∫D∂Q∂x-∂P∂ydA   Given: I=∫C3xy dx+6xy dy And C:…

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Q: Calculate ri(t) · r2(t)] and r.(t) × r2(t)] first by differentiating dt the product directly and…

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Q: Exercises Repeated Roots of Auxiliary Equation Find the general solution of the following: 3. (4D2 –…

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