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[Tamsvb9]

If anyone can solve these problems, please help me.

If x^3 + 2x^(2)y - 4y = 7, then when x=1, dy/dx=?


What is the area of the region between the graphs of y = x^3 and y = -x-1 from x=0 to x=2?


What is the average value of y=x^(3) *squareroot of (x^4 + 9) on the interval [0,2]?

 

[tkhunny]

Many have learned to solve such problems. Very often, the lEarning process involved showing someone else personal attempts at a solution. What have your attempts produced?

 

[stapel]

If x^3 + 2x^(2)y - 4y = 7, then when x=1, dy/dx=?

If this is in the section on implicit differentiation, then use that method. Otherwise, I would solve for "y=" and then differentiate as usual. Then evaluate y'(1).

What is the area of the region between the graphs of y = x^3 and y = -x-1 from x=0 to x=2?

Draw the graph. Which function is "above" the other? Use this as the upper limit and the other as the lower limit. Integrate over the interval from 0 to 2.

What is the average value of y=x^(3) *squareroot of (x^4 + 9) on the interval [0,2]?

Integrate to find the area. Then divide by the length to find the "average height".

If you get stuck, please reply showing your steps.

Thank you.

Eliz.