1) Find the value of limit |x|[cosx] where x tends to 0.. [.] is the Greatest integer function..
2) Find the value of limit (xy-yx)/(xx-yy) where x tends to y.
3) Find the solution of 2x+2|x|>= 2√2.
Please provide the proof...
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2 Answers
2621) [cosx]=0 (exactly) |x|→0+ hence limit=1
3) put two cases , x>0 and x<0
for x>0 , 2.2x ≥2√2 or, x≥1/2
for x<0 2x + 2-x >= 2√2 or , x ≤log2 (√2-1)
1in the second questn apply newtons leibentz theorem...
For differentiating xx,
take log both sides...
ln(y) = x ln(x)
1ydydx=lnx+1
proceed further and i obtain d answer as ...
1-lny1+lny