Category: Limits

Question Number 27701 by NECx last updated on 13/Jan/18 $$Ifthefunctionf\left(x\right)satisfies$$$$\underset{x\to 1}{\lim }\frac{f\left(x\right)-2}{x^2-1}=\pi ,evaluate\underset{x\to 1}{\lim }f\left(x\right)$$ Commented by abdo imad last updated on 21/Jan/18…

Question Number 27700 by NECx last updated on 13/Jan/18 $$iff\left(x\right)=\{\begin{array}{l}{mx}^2+n,x<0\\ nx+m,0⩽x⩽1\\ {nx}^3+m,x>1\end{array}$$$$forwhatintegersmandndoes$$$$both\underset{x\to 0}{\lim }f\left(x\right)and\underset{x\to 1}{\lim }f\left(x\right)exist?$$ Commented by NECx last updated…

Question Number 93200 by i jagooll last updated on 11/May/20 Commented by mathmax by abdo last updated on 11/May/20 $${let}\:{f}\left({x}\right)\:=\left(\mathrm{2}^{{x}} \:+\mathrm{3}^{{x}} −\mathrm{12}\right)^{{tan}\left(\frac{\pi{x}}{\mathrm{4}}\right)} \:\Rightarrow{ln}\left({f}\left({x}\right)\right)={tan}\left(\frac{\pi{x}}{\mathrm{4}}\right){ln}\left(\mathrm{2}^{{x}} \:+\mathrm{3}^{{x}} −\mathrm{12}\right)…

Question Number 27664 by abdo imad last updated on 12/Jan/18 $$letgivethesequence{V}_n=\prod _{k=1}^{k=n}{(1+\frac{k^2}{n^2})}^{\frac{1}{n}}$$$$findthevalueoflim{}_{n->\propto }{V}_n.$$ Commented by abdo…

Question Number 93146 by i jagooll last updated on 11/May/20 $$\underset{x\to 0}{\lim }\frac{\underset{0}{\stackrel{\mathrm{x}}{\int }}(\mathrm{a}+\mathrm{bcos}\mathrm{t}+\mathrm{c}\cos \left(2\mathrm{t}\right))\mathrm{dt}}{{\mathrm{x}}^5}=15$$ Commented by i jagooll last updated on 11/May/20…