Compute delta(y) and dy for the given values of x and dx=delta(x)
y=x^2 , x=8 , delta(x)=0.5
Delta(y)= ???
dy = ???
I got dy=8 by doing:
dy= (f prime of x)dx
dy=2xdx
dy=2xdelta(x)
dy=2*8*0.5
dy=8
but I have not clue how to find delta(y) please help!
deltay = y(x+deltax)- y(x)
= (8.5)^2 - (8)^2
= (8 + 1/2)^2 - 8^2
= 8^2 + 8 + 1/4 - 8^2= 8.25
check my work.
thanks!
Great job on finding dy! Now let's move on to finding delta(y).
To find delta(y), we need to use the formula:
delta(y) = y(x + delta(x)) - y(x)
Given that y = x^2, x = 8, and delta(x) = 0.5, we can substitute these values into the formula:
delta(y) = (8 + 0.5)^2 - (8)^2
= 8.5^2 - 8^2
= 72.25 - 64
= 8.25
Therefore, delta(y) is 8.25.
You can also verify the result by using the numbers you calculated for dy:
dy = 8
Since delta(y) represents the change in y, and dy also represents the change in y, delta(y) should be equal to dy.
In this case, delta(y) = dy = 8.
So, both methods yield the same result, confirming that delta(y) is indeed 8.25.
I hope this helps! Let me know if you have any further questions.