Last Amath question before the exams ! XD

davidche SG

Find, in terms of p, the approximate change in curve tan(2x+1) as x increases from 1 to 1+p, where p is small. Note that tan(2x+1) has no stationary point as its dydx cannot be 0

skythewood SG

remember the radian thing? apply that. remember the tan p = p if p is very small? apply that.

so use your angle addition rule for tan (x +p) = (tan+tan)/(1 + tantan) thingie.

and sub in your tan p = p.

hisoka SG

tot is just differentiate tan(2x+1)?

davidche SG

tot is just differentiate tan(2x+1)?

u get 2 (sec 2x+1)^2

Then what>?

skythewood SG

for x, when 1 ==> 1 + p,

tan (2(1) +1) ==> tan (2(1+p) +1)

tan (3) ==> tan ( 3 + 2p)

==> (tan3 + tan 2p) / [1 + tan(3)tan(2p)]

let tan p = p since p is small.

==> (tan3 + 2p) / [1 + tan(3)2p]

change = final - initial

= (tan3 + 2p) / [1 + tan(3)2p] - tan (3)

go clean it up more.

davidche SG

for x, when 1 ==> 1 + p, this is because since p is so small it doesnt matter?

let tan p = p since p is small. -> i never knew this XD

skythewood SG

this is for radian approximation...

1 ==> 1+p

is my way of saying as 1 approaches 1+p,

than the next line explains what happens to tan(2x + 1) when this approximation happens.

if this is out of your syllabus, than just skip this thingie bah.

davidche SG

this is for radian approximation...

1 ==> 1+p

is my way of saying as 1 approaches 1+p,

than the next line explains what happens to tan(2x + 1) when this approximation happens.

if this is out of your syllabus, than just skip this thingie bah.

the tys answers required you to differentiate first.

Ill give you the solution cos i cant understand what the sol. means here it is:

x=1

8x= p

dydx = 2 (sec (2x+1))^2

= 3 (sec 3) ^2

8y = 2 (sec 3)^2 * p

= 2.04p

care to xplain? thanks

skythewood SG

that looks really... exact.

approximation?

skythewood SG

approx the tan curve to be straight line with gradient 2 (sec (2x+1))^2 = 2.04

using simple forumla Y = mX + C.

when x = 1, Y = something...

when x = 1+ p, Y = something + 2.04p