2) Find the cartesian eauation for the olar curve r=tan e sece ×ニy )yニxと 2.

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Q: 2) Calculate lim ( In(3x + 1) – In(2x + 1)). -

A: Since you have asked multiple questions, we will solve the first question i.e., Question-(2) for…

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A: The rules of KenKen puzzle is: Use each number only once per row, once per column. Cages with just…

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Q: lim - Va +1

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Q: Q5/Find the Laplace Transform 3-f(t) = sint cos t

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Q: The equation of the sphere with radius r = V75 and center C(2,1, – 1) is (a) x² + y² + z² + 4x + 2y…

A: The general equation of a sphere with radius r and center a,b,c is x-a2 + y-b2 + z-c2 = r2

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Q: Q4/Find The Inverse Laplace Transform By Partial 3s-12 Fraction (s-1) (s2 +8)

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A: We have to find the values of x and y from the above expression.

Q: Find the second-order partial derivatives of the function. Show that the mixed partial derivatives…

A: Given: Now, fxx=∂2∂ x2x5+x2y2+y5+x+y    =∂ ∂ x5x4+2xy2+1    =20x3+2y2 fyy=∂2∂ y2x5+x2y2+y5+x+y…

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Q: _12. What is the maximum directional derivative Daf of the function f(x,y,z) = x – y² + z² at the…

A: Let's find.

Q: Using Integration By Parts, 2x² e3" dx = u v - |2x2 e3" dx = u v-, -Svau Find u v- Sv du · x3 e 3 dx…

A: Integral

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A: Solution is given below:

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A: We can solve as follows

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Q: cot ve csc² Ve do 3 Vo (4 + cot? Ve)

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Q: 4. sin2 -x | dx. Use trigonometric groups. 2 X| cos

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Q: 1. S(5x4 + 2x – 1)dx 2. S dx. 3. 늘e-ndx 4. S cot?x dx In 4x 5. S A dx

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Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Let θ denote the angle between thw ladder and the ground

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Q: 5. Let ƒ be a function satisfying the following properties: lim f(r) = 2 continuous on R \ {0} •…

A: a. Here, we have  limx→0-fx=-∞, which means the function has a vertical asymptote x=0; limx→+∞fx=0…

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A: Let's find.

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A: Since you have asked multiple questions in a single request we would be answering only the first…

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Q: Find the total area enclosed between y = x and y = x over th- %3D interval [-1,6]. NOTE: Enter the…

A: Here, to find the area enclosed by y=x3 and y=x over the interval [-1,6].