Find the differential dy: y = sin(av). dy = " cos (av) [2v + a+i In a (1 + Ina p + x!+ In ¤ (1+ ln ¤) dæ dy = cos (2v) (2v + a*i In a) dze (E) None of these choices O dy = cos (av) 2v# + »+ In a + sin(av= In a + sin (zv) d COS

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A: To solve the given equation algebraically

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A: To determine whether the given statement is true or false.

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Q: ) (2xy+y2) dx - 2x2 dy = o 2) xy dx-(x + zy)? dy = o メ+ 2y)? dy

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A: As per the guidelines I can solve only first question

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A: Solving

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A: As per our guidelines we can help you in solving only first problem rest of the problems you have to…

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A: Let's find.

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A: We can solve as follows

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Q: cos2x dx sinx

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Q: a) Determine whether the series 11n? + 8n + 32 is n³ + 3n2 – 7n + 1 n=1 RY convergent or divergent.

A: Since you have posted multiple questions which are not interlinked i can do first question as per…

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A: Write the nth term and  add them to get Sn .

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A: Given :

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Q: completely

A: We will solve the integration.

Q: Find r'(t). r(t) = (tan-'(5t))i+t cos(t)j – Vik NOTE: Enter your answer in terms of i, j, and k.

A: r(t)=tan-1(5t) i+t cost j -t kddt tan-1(5t)= 11+(5t)2 ddt(5t)ddt tan-1(5t)= 51+25t2 ddtt cost=cost-t…

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A: Find your answer below

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A: Given: rt=tan-15ti+tcostj-tk

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A: We will put the x values and get the f(x) values.

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A: We will solve the integral.

Q: Find V · (V × F) if F(x, y, z) = 2 sin xi+ 8 cos(4.x – 5y)j + 2zk. %3D - V·(V × F) = %3D

A: Given :F(x,y,z)=2 sin xi+8 cos(4x-5y)j+2zkTo find : ∇·(∇×F)