Question

V^2=2gh
use calculus, if g increase by 5% and h decrease by 10% find the percentage change in V

Answer 1

@ganeshie8 hmm

Answer 2

??

Answer 3

calculus?

Answer 4

yes

Answer 5

then i must be reading this wrong

Answer 6

take log and differentiate
dh is delta H
the you can use percentages

Answer 7

then*

Answer 8

i get \[V^2=2(1.05)g(1.1)h\]

Answer 9

can you do it out

Answer 10

because i really dont know how to write it out

Answer 11

if g increase by 5%\[g\to 1.05g\]

Answer 12

yep but how to do it in calculus

Answer 13

i think i do not understand this question, so i will be quiet

Answer 14

oooh maybe it is this
\[2VV'=2(hh'+gg')\] then plug in \(h'=.05,g'=1.1\)
does that seem reasonable?

Answer 15

g is decreasing so it think that would be g'= 0.90

Answer 16

h0.9 and g 1.05?

Answer 17

sorry h' = 0.90

Answer 18

oh right i read it wrong sorry

Answer 19

hmm not sure about that though, since \(h'\) is the rate of change
in my original method, yes, but here i guess \(h'=-.1\)

Answer 20

2 log V = log g + log h
differentiating
\[ 2\Delta V / V = \Delta g /g + \Delta h /h\]

Answer 21

del g /g = 0.05
and del h / h = 0.1