3. a) Find polar coordinates (r, 0) of the point (1, -/3), where r> 0 and 0 <0 < 2 p2 = x² + y?, tan 0 = y/x

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A: We can evaluate the answer as below.

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A: Concave up if f"(x)&gt;0 Concave down if f"(x)&lt;0

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A: Differentiate with respect to x.  According to guidelines we solve only first three parts. 

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A: we will use nth derivative formula of cosx .

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Q: The Range of y = V9- Vã /x is

A: The function y= √(a-x) is valid for all real     x ≤ a and range of this function is [0,√a]

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

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A: Evaluate indefinite integral.

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A: This question can be solved by first plotting the graphs to get the feel of the area enclosed.

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A: This question is based on Use of Dot product and cross product.

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A: I am attaching image so that you understand each and every step.

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A:   X Y XY X2 Y2   1 2 2 1 4   3 4 12 9 16   5 7 35 25 49 sum 9 13 49 35 69     X¯ =1n Σ Xi...

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A: To evaluate the given integral.

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A: Please see the answer below.

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A: Here, f(x)=5x8+2x2+2sin(x)-2-x8+5x+5

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A: a.Solution :2i68-3i-89+4i114we know that i2=-1i3=-ii4=12i17×4-3i-22×4+1+4i28×4+22i17×4-3i22×4+1+4i28...

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A: The volume of the parallelepiped spanned by vectors a→, b →and c→ is given by a→×b→·c→ We know that ...