24Q2\lim_{x\rightarrow infinity}48x(\frac{\pi }{4}-tan^{-1}\frac{x+1}{x+2})
Q1\lim_{x\rightarrow 1}\frac{x^{x}-1}{xlogx}-\lim_{x\rightarrow 0}\frac{log(1-3x)}{x}
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7 Answers
24
1Q.1) first part- limx→1 xx-1/xlogx
using L hospital limx→1 xxx-1/logx+1
=1
second part limx→0 (-3x)log(1+(-3x))/(x)(-3x)
= -3
1-(-3)=4
1A2) Let x=1/h
Then the limit becomes
\lim_{h\rightarrow0}48\frac{(\frac{\pi}{4}-\tan^{-1}\frac{1+1/h}{1+1/2h})}{h}
Which can b simplified using LH
62write
(x+1)/(x+2) = 1- 1/(x+2)
that will probably make 2nd much simpler!
24@ amit and rkrish.......i know it can be dune by LH rule..i posted it here becoz i am looking for some other method by which it can be solved...becoz LH rule always isnt the best option[1][1]
11Q1
IF U DISLIKE LH
SO EXPANSIONS R WAITING 4 UR ATTENTION[6]
Q2 NISHANT SIR SAID IT ALL IN#6
I THINK NOW IT DOES NOT NEED ANY SIMPLER JUSTIFICATION[1]