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Question Number 58576 by Mikael_Marshall last updated on 25/Apr/19

$$\underset{x\to \mathrm{\infty }}{lim}\frac{{(x-20)}^{70}.{(2x+3)}^{30}}{{(4x-1)}^{15}.(5-x^{85})}$$

Answered by tanmay last updated on 25/Apr/19

$$\underset{x\to \mathrm{\infty }}{\lim }\frac{x^{70}{(1-\frac{20}{x})}^{70}\times 2^{30}\times x^{30}{(1+\frac{3}{2x})}^{30}}{4^{15}\times x^{15}{(1-\frac{1}{4x})}^{15}\times x^{85}(\frac{5}{x^{85}}-1)}$$$$\underset{x\to \mathrm{\infty }}{\lim }\frac{x^{100}\times 2^{30}\times {(1-\frac{20}{x})}^{70}{(1+\frac{3}{2x})}^{30}}{4^{15}\times x^{100}\times {(1-\frac{1}{4x})}^{15}(\frac{5}{x^{85}}-1)}$$$$\frac{2^{30}}{2^{30}}\times \frac{{(1-0)}^{70}\times {(1+0)}^{30}}{{(1-0)}^{15}\times (0-1)}$$$$=\frac{1}{-1}=-1$$

Commented by Mikael_Marshall last updated on 25/Apr/19

$$thankyouSir.$$

Answered by Prithwish sen last updated on 25/Apr/19

$$=\mathrm{li}\underset{\mathrm{x}\to \mathrm{\infty }}{\mathrm{m}}\frac{{\mathrm{x}}^{70}{(1-\frac{20}{\mathrm{x}})}^{70}{\mathrm{x}}^{30}{(2+\frac{3}{\mathrm{x}})}^{30}}{{\mathrm{x}}^{15}{(4-\frac{1}{\mathrm{x}})}^{15}{\mathrm{x}}^{85}{(\frac{5}{{\mathrm{x}}^{85}}-1)}^{}}$$$$=-\frac{1.2^{30}}{4^{15}.1}$$$$=-1$$$$$$

Commented by tanmay last updated on 25/Apr/19

$$sirithink$$$$=\frac{1\times 2^{30}}{4^{15}\times -1}=-1$$$$plscheck$$

Commented by Mikael_Marshall last updated on 25/Apr/19

$$thanksSir$$

Commented by Prithwish sen last updated on 25/Apr/19

$$\mathrm{Yes},\mathrm{I}\mathrm{make}\mathrm{a}\mathrm{mistake}.\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}.$$

Commented by tanmay last updated on 25/Apr/19

$$sir..ihaveaideaforthisforum...canweselect$$$$topicphysics/mathonaparticulardaythen$$$$postquestiononthattopicsandsolve/discuss$$$$takinghelpofgoodbook.Tanmay$$$$$$$$$$$$$$

Commented by Mikael_Marshall last updated on 25/Apr/19

$${it}^{\prime }sagreatideaSir.$$

Commented by Prithwish sen last updated on 25/Apr/19

$$\mathrm{Agree}$$

Commented by malwaan last updated on 26/Apr/19

$$Fantasticidea$$$$Iagreewithyou$$

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