3answer ta ki....2/3??
lim 2.x1/2 +3.x1/3 +4.x1/4+..........+n.x1/n
x→∞ (3x-4)1/2+(3x-4)1/3+..........+(3x-4)1/n
(WITHOUT USING L-HOSPITAL)
plzzzzzzzzzz HELPPPP!!!!
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7 Answers
1\lim_{h\rightarrow 0}\frac{2\left(\frac{1}{h^{1/2}} \right)+3\left(\frac{1}{h^{3/2}} \right)+.......+n\left(\frac{1}{h^{1/n}} \right)}{(3-4h)^{1/2}+h^{\left(\frac{1}{2}-\frac{1}{3}\right)}(3-4h)^{1/3} +....+h^{\left(\frac{1}{2}-\frac{1}{n} \right)}(3-4h)^{1/n}}
[ on putting x=1/h as x →∞ , h→ 0 ]
\lim_{h\rightarrow 0}\frac{2+3h^{\left(\frac{1}{2}-\frac{1}{3} \right)}+4h^{\left(\frac{1}{2}-\frac{1}{4} \right)}+.....+nh^{\left(\frac{1}{2} -\frac{1}{n}\right)}}{(3-4h)^{1/2}+h^{\left(\frac{1}{2}-\frac{1}{3} \right)}(3-4h)^{1/3}+.....+h^{\left(\frac{1}{2} -\frac{1}{n}\right)}(3-4h)^{1/n}}
now u can solve i guess
answer comes be 2√3 by substituting h as 0
1i don't thnk e2 is the answr check again.there is nothng wrong in my process is it ??
3ya the answer is 2/√3......i made a slight mistake by neglcting the root :)