Category: Limits

Question Number 115318 by bemath last updated on 25/Sep/20 $$\underset{x\to 0}{\lim }\frac{x\sin x}{2\sin {}^2\left(3x\right)-x^2\cos x}$$ Answered by bobhans last updated on 25/Sep/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\:\mathrm{sin}\:{x}}{\mathrm{2}\:\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{3}{x}\right)−{x}^{\mathrm{2}}…

Question Number 115195 by bemath last updated on 24/Sep/20 $$\underset{x\to \frac{\pi }{8}}{\lim }\frac{\cot 4x-\cos 4x}{{(\pi -8x)}^3}?$$ Answered by bobhans last updated on 24/Sep/20 $$letx=\frac{\pi }{8}+p;p\to 0$$$$\underset{{p}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cot}\:\left(\mathrm{4}{p}+\frac{\pi}{\mathrm{2}}\right)−\mathrm{cos}\:\left(\mathrm{4}{p}+\frac{\pi}{\mathrm{2}}\right)}{\left(−\mathrm{8}{p}\right)^{\mathrm{3}}…

Question Number 115167 by bemath last updated on 28/Sep/20 $$\underset{x\to 0}{\lim }\frac{\sec \left({\sin }^{-1}(1-x)\right)}{3\sqrt{x}}=?$$ Answered by bobhans last updated on 28/Sep/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sec}\:\:\left(\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{1}−{x}\right)\right)}{\mathrm{3}\sqrt{{x}}}\:=? \…

Question Number 115122 by bobhans last updated on 23/Sep/20 $$\underset{x\to \mathrm{\infty }}{\lim }\sqrt{(x^2+2x)(x^2+1)}-\sqrt{(x^2+2x)(x^2+4)}?$$ Commented by malwan last updated on 23/Sep/20 $${can}\:{we}\:{solve}\:{it}\:{with}\:{lhopital}??…

Question Number 115027 by bemath last updated on 23/Sep/20 $$\mathrm{If}\underset{x\to 3}{\lim }\frac{17\sqrt[3]{\mathrm{ax}+3}+\mathrm{b}}{\mathrm{x}-3}=\frac{136}{27}$$$$\mathrm{then}8\mathrm{a}+\mathrm{b}=?$$ Answered by bobhans last updated on 23/Sep/20 $$limitform\frac{0}{0}.numeratormustbe=0$$$$\left(\mathrm{1}\right)\:\mathrm{17}\:\sqrt[{\mathrm{3}\:}]{\mathrm{3}{a}+\mathrm{3}}\:+{b}\:=\mathrm{0};\:\:{b}\:\Rightarrow−\mathrm{17}\:\sqrt[{\mathrm{3}\:}]{\mathrm{3}{a}+\mathrm{3}}…