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Limx→∞x2+3x1+2x2 \operatorname{Lim}_{x \rightarrow \infty} \frac{x^{2} + 3 x}{1 + 2 x^{2}} Limx→∞1+2x2x2+3x এর মান কোনটি ?
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limx→∞x2+3x1+2x2 \lim _{x \rightarrow \infty} \frac{x^{2}+3 x}{1+2 x^{2}} limx→∞1+2x2x2+3x
=limx→∞x2(1+3x)x2(1x2+2)=limx→∞1+3x1x2+2=1+3∞1∞+2=1+00+2=12 \begin{array}{l} =\lim _{x \rightarrow \infty} \frac{x^{2}\left(1+\frac{3}{x}\right)}{x^{2}\left(\frac{1}{x^{2}}+2\right)}=\lim _{x \rightarrow \infty} \frac{1+\frac{3}{x}}{\frac{1}{x^{2}}+2} \\ =\frac{1+\frac{3}{\infty}}{\frac{1}{\infty}+2}=\frac{1+0}{0+2}=\frac{1}{2} \end{array} =limx→∞x2(x21+2)x2(1+x3)=limx→∞x21+21+x3=∞1+21+∞3=0+21+0=21
limx→0(1−cos2x)sin5xx2sin3x=?\displaystyle\lim_{x\rightarrow 0}\dfrac{(1-\cos 2x)\sin 5x}{x^2\sin 3x}=?x→0limx2sin3x(1−cos2x)sin5x=?
limx→π/2sinx−(sinx)sinx1−sinx+Insinx\displaystyle\lim_{x\to \pi/2} \dfrac{sinx-(sinx)^{sin x}}{1-sin x + In sin x}x→π/2lim1−sinx+Insinxsinx−(sinx)sinx is equal to-
The values of limn→∞n5+24−n2+13n4+25−n3+12\displaystyle\lim_{n\rightarrow \infty}\dfrac{\sqrt[4]{n^5+2}-\sqrt[3]{n^2+1}}{\sqrt[5]{n^4+2}-\sqrt[2]{n^3+1}}n→∞lim5n4+2−2n3+14n5+2−3n2+1 is?
limx→0+(cosecx)1/logx\displaystyle \lim_{x\rightarrow 0^{+}}{(\cosec x)^{1/\log x}}x→0+lim(cosecx)1/logx=?
