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Category: Limits

If-n-1-a-n-is-convergent-and-n-1-b-n-is-convergent-What-are-the-sufficient-condition-so-that-n-1-a-n-n-b-n-1-n-converges-a-n-b-n-gt-0-

Question Number 3460 by prakash jain last updated on 14/Dec/15 $$\mathrm{If}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{a}_{{n}} \:\mathrm{is}\:\mathrm{convergent}\:\mathrm{and}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{b}_{{n}} \:\mathrm{is}\:\mathrm{convergent}. \\ $$$$\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{sufficient}\:\mathrm{condition}\:\mathrm{so}\:\mathrm{that} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{a}_{{n}} ^{{n}} {b}_{{n}}…

Question-68965

Question Number 68965 by anaplak last updated on 17/Sep/19 Commented by anaplak last updated on 17/Sep/19 $${sir}\:{please}\:{give}\:{me}\:{the}\:{solution}\:{showing}\:{by}\:{taking}\:{right}\:{hand}\:{limit}\: \\ $$$${i}\:{mean}\:{to}\:{say}\:{in}\:{detailed} \\ $$ Commented by kaivan.ahmadi last…

lim-x-8-x-1-3-2-x-2-2-

Question Number 134173 by mathlove last updated on 28/Feb/21 $$\underset{{x}\rightarrow\mathrm{8}} {\mathrm{lim}}\frac{\sqrt[{\mathrm{3}}]{{x}}−\mathrm{2}}{\:\sqrt{{x}}−\mathrm{2}\sqrt{\mathrm{2}}}=? \\ $$ Answered by malwan last updated on 28/Feb/21 $$\underset{{x}\rightarrow\mathrm{8}} {{lim}}\:\frac{\:^{\mathrm{3}} \sqrt{{x}}−\mathrm{2}}{\:\sqrt{{x}}−\mathrm{2}\sqrt{\mathrm{2}}}×\frac{\:^{\mathrm{3}} \sqrt{{x}^{\mathrm{2}} }+\mathrm{2}\:^{\mathrm{3}}…

lim-x-0-1-sin-x-cos-x-1-sin-px-cos-px-

Question Number 134171 by liberty last updated on 28/Feb/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}+\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}}{\mathrm{1}+\mathrm{sin}\:\left(\mathrm{px}\right)−\mathrm{cos}\:\left(\mathrm{px}\right)}\:=? \\ $$ Answered by malwan last updated on 28/Feb/21 $$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{\mathrm{1}+\left({x}−…\right)−\left(\mathrm{1}−…\right)}{\mathrm{1}+\left({px}−…\right)−\left(\mathrm{1}−…\right)}\:\:=\:\frac{\mathrm{1}}{{p}} \\ $$ Answered…