Question

find y^2 + 1/y^2 and y^4+1/y^4 if y-1^y2/y =9 plz fast

Answer 1

The question was .. A curve is represented by y = 1000(lnx).What is the approximate change in y, when x changes from 10 to 10.05 ?

What I did -

Let Y1 and Y2 be the value of y at x = 10 and 10.05 respectively ..

Therefore

Y1 = ln 10 ^1000 - eq 1

And

Y2 = ln (10.05)^1000 - eq 2

Or Y2 = ln (10 + 0.05)^1000

Or Y2 = ln [10^1000(1 + 0.005)^1000]

By binomial approximation

Y2 = ln [ 10^1000(1 + 5)]

Y2 = ln [10^1000] + ln 6 - eq 3

Now eq1 - eq3 = Delta y

=> Delta y = {ln 10^1000 + ln 6} - {ln 10^1000}

=> Delta y = ln 6

=> Delta y = 1.79 app

But this and is wrong

And if I directly find Delta y .. ie

Eq 1 - eq 2 = Delta y

=> Delta y = {ln (10.05)^1000} - {ln(10^1000)}

=> Delta y = ln [(10.05/10)^1000]

=> Delta y = 1000 ln (1.005)

=> Delta y = 1000*0.00498

=> Delta y = 5 appx

Which is correct .. plz explain