Solve the differential equation (1 + y² + xy²) dx + (x²y + y + 2xy) dy = 0 ɑ. 2y+x²(1+x)² = C b. 2x + x²(1+y)² = C c. 2x + y² (1+x)² = C d. 2y + y² (1+ y)² = C

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A: Question: If the relation represents a function, find the domain and range. (have it in interval…

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A: Solution is given below:

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A: Graph

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Q: 5. dy/dx = sin(x + y). ANS. x+c = tan (x + y). sec (x + y).

A: Please see the below picture for detailed solution.

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A: Average value of a function y=f(x)  from x=a to x=b is given by Aavg=1b-a∫x=ax=bf(x)dxsee below the…

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A: Given: Now,           y' +y=y2⇒dyy2-y=dtIntegrating both sides we get,⇒y=11-et+c1

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Q: 12. Determine whether the following is true: (a) ≥3, EZ, 31(2²" - 1); n (n + 1)(2n +1) (b) 12+22+ 32…

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A: Given integral:- ∫251x-2dx

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A: Topic:- calculus       Definition:- If the second derivative of a function is negative on some…

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Q: it got marked wrong? did i type it in wrong?

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A: Please see the below picture for detailed solution.

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A: Here we have to find the values of f(x).

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Q: -3. For the function f(x) = -5x - 3, find the slope of the tangent line at x =

A: We can find the slope in the following steps.

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Q: 1. (a) Use the Euclidean Algorithm to find ged(125, 793). (b) Using the workings in (a), find m, n €…

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A: The objective is to use interval notation to determine where f(x)&gt;0. 2 and use interval notation…

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A: Given ∫022x2+5xdx

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A: We can solve this as follows:

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A: Note: Since the student has posted 2 sub-parts of the question in which the part (1) is complete and…

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A: To find slope of a line tangent to the given curve at a given point. To make a sketch of this…

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Q: 4. The population, P, of a school of fish t years after being released in a new habitat is given by…

A: The solution is given below