Question

Let y=2sqrtx .
Find the change in y, deltay when x=5 and deltax=0.4
Find the differential dy when x=5 and dx=0.4

Answer 1

\[y=2\sqrt x\]
Can you find \(\frac{dy}{dx}\)?

Answer 2

yeah i got x^-1/2dx

Answer 3

good, so
\[\large \frac{dy}{dx}=(x)^{-\frac 12}\]
Find the change in y when
"deltay when x=5 and deltax=0.4"
so
\[dx=0.4\]
\[x=5\]
find value of dy? just plugin the no.s

Answer 4

Do the same thing as last time :) just don't forget the dx :P

Answer 5

i got dy=0.178885 is that correct

Answer 6

That's right.

Answer 7

you're right

Answer 8

dy when x=5 and dx=0.4

i'd guess this one is meant to be 0.04 again. So just plug in 0.04 as dx this time.

Answer 9

no i think we have to do something else cause its asking for the change in y i wanted to use an equation i saw in class its
f(x+delta x)-f(x)

Answer 10

The change in y *is* the delta y. Delta means change.

Answer 11

Oh i think i see what you mean, though.

Answer 12

\[\frac{f(x+\Delta x)-f(x)}{(x+\Delta x-x)}=f'(x) \]

Answer 13

yeah i just used that equation and i got it right thanks you i just had to find i guess is the distance that x had change

Answer 14

Oh yeah i think you wanted the amount y changed to, ie the initial and final y. Not the actual dy.

Answer 15

yeah thats what it is well thanks!! :)

Answer 16

For that, yes you just add dy to whatever y is when x=5.