Differenciation?

Question

Given that y=2+(8/x), find the approx. change in x which will cause y to change from 6.0 to 6.01

Yes this is calculus, I know that ;)
Anybody else????

Answer 1

differentiating both sides with respect to x, dy/dx = -8/x^2.

y = 6. Therefore, x = 8/(y-2) = 2.
dy = 0.01 = -8/(x^2) * dx = -2*dx
=> dx = -0.01/2 = -0.005

Therefore x needs to be reduced by 0.005 in order to increase y by 0.01.

Answer 2

Let us find x for which y=6.0

6 = 2+(8/x)

4 = 8/x

4x = 8

x = 2

Now, let h be the change from x

6.1 - y = 2 + 8/(x + h) - (2 + 8/x)

Because x=2 and y=2 + 8/x \ 6 = 6

6.1 - 6.0 = 2 + 8/(2 + h) - 6.0 // add 6.0

6.1 = 2 + 8/(2 + h) // subtract 2

4.1 = 8/(2 + h) // multiply by 2+h

8.2 + 4.1h = 8 // subtract 8.2

4.1h = -0.2 // divide by 4.1

h = -2/41 = -0.04678.... approximately -0.05

Answer 3

I think we can do this without calculus:-
6 = 2 + 8/x1
6x1 = 2x1 + 8
4x1 = 8
x1 = 2

6.01 = 2 + 8/x2
6 .01x2 = 2x2 + 8
4.01x2 = 8
x2 = 1.995
Change in x is 2 - 1.995 = 0.005

Answer 4

y=2+8/x
when y=6 , x=2

dy/dx= -8/x^2

at x=2, dy/dx= -8/4=-2

aproximately (change in x)=(change in y) / (dy/dx)
=0.01/(-2) =-0.005

Answer 5

permit m signify what number cos[x consequently 4 f cos4x could be cos mx Then for any fee of m the by-product is - msinmx consequently - 4 sin 4x...........comparable as Robert's answer occasion by-product of cos5x is - 5 sin 5x it is shown employing chain rule For sin4x by-product is 4 cos 4x