InterviewSolution
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InterviewSolution
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Thefunction `f:""R""~""{0}vecR`given by`f(x)=1/x-2/(e^(2x)-1)`can be made continuous at x = 0 by definingf(0) as(1)2(2) `-1`(3) 0(4) 1 |
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Answer» Correct Answer - B For f(x) to be continous at x=0, we must have gtbrgt `f(0)=underset(x to 0)lim f(x)` `Rightarrow f(0)=underset(xto 0) lim ((1)/(x)-(2)/(e^(2x)-1))` `Rightarrow f(0)=underset(xto 0) lim (e^(2x)-1-2x)/(x(e^(2x)-1))` `Rightarrow f(0)=underset(xto 0) lim ((1+2x+((2x)^(2))/(3!)+....)-1-2x)/((x+(1+2x+)(2x)^(2)/(2!)+.....-1))` `Rightarrow f(0)=underset(xto 0) lim ((2x)^(2) {(1)/(2!)+(2x)/(3!)...})/(x{2x+((2x)^(2))/(2!)+...})` `Rightarrow f(0)=underset(xto 0) lim (2{(1)/(2!)+(2x)/(3!)...})/({1+(2x)/(2!)+...})=2xx(1)/(2)=1` |
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