ISI 2011 doubt

[manisha]

can anyone please explain Q-3,Q-4 and Q-20

[The Villain]

Forvquest 4 ...draw the 3 graphs and highlight the max oart...there will not be ny break pt so no pt of discontinuity

[The Villain]

q3...ln2/ln4-ln2/ln8+........
ln2/2ln 2-ln 2/3ln 2+.......
ln 2/ln 2(1/2-1/3+1/4....
...
.
.solve this...u will get ans as1-ln 2

[manisha]

please explain this part- ln2/ln 2(1/2-1/3+1/4....

[Granpa Simpson]

use expansion of log(1+x), here x=1...and ul get the answer..!!!

[Granpa Simpson]

for 4) define the function as f(x)=x, when x<0, f(x)=x^2 when 0<=x<1 and f(x)=1, 1<=x<infinity...check weder the function is continuous at x=0,1...at x=0, f(0-)=f(0+)=0...similarly at x=1, f(1-)=f(1+)=1...hence the function is continuous at x=0 and x=1...thus the function is continuous for every x in R...also u can draw the graph and check..!!!