Question

A) If x^2+y^3−xy^2=5, find dy/dx in terms of x and y.
dy/dx=________

B) Using your answer for dy/dx, fill in the following table of approximate y-values of points on the curve near x=1 y=2.

0.96 ______
0.98 ______
1.02 ______
1.04 ______


C) Finally, find the y-value for x=0.96 by substituting x=0.96 in the original equation and solving for y using a computer or calculator.
y(0.96)= ________

D) How large (in magnitude) is the difference between your estimate for y(0.96) using dy/dx and your solution with a computer or calculator?
___________

Answer 1

I am not going to do this for you. What are you stuck on, or don't understand?

Answer 2

In the first part... I got (-2x+y^2)/(3y^2+x2y) but apparently that's wrong which will make everything else wrong.... I just need to know how to do that part right...

Answer 3

I see what is wrong with my equation... now I have (-2x+y^2)/(3y^2-x2y) and for the second part I tried to plug 1 for x and all the other values for y and then in the third part I plugged 2 for y and 0.96 for x and I got them all wrong:

my values are:
0.96 = -1.2765
0.98= -1.1285
1.02= -0.8875
1.04= -0.7885

and for part C) 0.255
and For part D) -1.5315