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lim x^x is 1 (by taking log and then using LH rule )
so x^x^x = 0

ans is -1

there are in general no shortcuts in indefinite integration
but u will find many shortcuts in Definite Integrals

yaar ye 2 ke neeche dabba kyun laga rakha hai????

There are many factors which explain the answer to your ques.

1. A good nucleophile in general is a good leaving group.
2. A good leaving group is one which is able to stabilize itself. It is observed that a weak base is a good leaving group
3. Among halides ions, I- is the weakest base and hence a good leaving group.
4. A good leaving group cannot however decide whether a rxn will be SN1 or SN2.
5. Stronger is the nucleophile, more is the chance for SN2 mechanism
(Large and easily polarized groups are stronger nucleophiles: HS-, I-, CH3COO-)
6. Elimination occurs if the temp is higher than the normal temp or there is stearic hindrances either in substrate or reagent.
7. Naturally a good base say RO- will seek for H+ and cause elimination. Other strong bases can be visualized by their conjugate acids strength.Eg OH ion is strong base bcoz H20 is weak acid(pH=7)

You are a bit confused. koi baat nahin

Locus means "path"

and path is for a point

so for a point which is alwayz equidistant from a fixed point say(-g,-f) and the dist is R

then locus is a circle of the radius R

you can get the equation of the locus by using the distance formula

is the ans R/2 ??

differentiate each term separately
then put x=1
1st term =A
logA=sin(pi.x/2)logsiny
diff wrt x
get dA/dx
2nd term is easy to diff
3rd term use product rule and chainrule

use reduction formula

from maths forum in goiit
Simple!!!

Re:what is the period of the function sin pi{x} where {x} is the fractional part of x

bhaiya y=x line par agar x=0 hota hai to kya dy/dx bhi zero ho jata hai
Nahin na..
woh to one hi hota hai
isliye agar v=0 ho to zaruri nai hai k field bhi zero ho

dy/dx = (1+logx)y

agn differentiate

d²Y / dX^{2 =}dy/dx (1+logx) +y/x

marked thing can be substituted frm topmost eqn

you will get the answr

y=X^X ka log leke diffrentiate karde do bar
aajayega aaram se

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