SUBJECT: DIFFERENTIAL CALCULUS NOTE: Make the solution detailed and clear in a sheet of paper. 1. A jet plane is flying west at 5 feet per sec at an altitude of 4000 feet.  The plane is in vertical plane with a search light on the ground.  If the light is to be kept on the plane, how fast is the search light revolving (dƟ / dt  in radians per sec ) when the jet plane is due east of the search light at an airline distance of 2000 feet.

Q: Find the instantaneous rate of change for the function at the given value. f(x) = x² + 3x at x = 0…

A: We can find the instantaneous rate of change as below

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A: To find the particular solution for the given DE.y''-5y'=x-2, when x=0, y=0, y'=2

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A: We have to solve given Questions.

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A: Explanation of the answer is as follows

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A: Please see the below picture for detailed solution.

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A: Given: A=30-1211, C=142315

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A: Taylor series function y=8xex at x=0

Q: 1. Solve the following equations: c) (x² - 4xy – 2y²) dx + (y² + 4xy – 2x²) dy = 0 -

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A: topic - strictly  decreasing  interval of function

Q: 2. S dx x²-x+2

A: Given problem:-

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Q: In2 fin² coshx dx

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A: We know that integration of xn is xn+1/n+1.     Here i attached the solution of this question.

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A: To find the laplace transform of the given function.

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Q: Find the critical point and the intervals on which the function is increasing or decreasing and…

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Q: 10. Determine the surface area of the part of z = xy that lies in the cylinder given by x² + y² = 1.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

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Q: A smooth vector-valued function R(t) satisfies R(1) = (-3,7,9), R'(1) = (0,5,6) and R'(1) = (4, 1,…

A: Explanation of the answer is as follows

Q: zl 5. Trigonometric form of the quotient of = 6cis (2); z2 = 2cis () is:

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