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Limx→0ex+1−2e3xx \operatorname{Lim}_{x \to 0} \frac{e^{x}+1 - 2 e^{3 x} }{x} Limx→0xex+1−2e3x এর মান কত?
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-5
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limx→0ex+1−2e3xx[00]=limx→0ex−6e3x1=1−6=−5 \begin{aligned} & \lim _{x \rightarrow 0} \frac{e^{x}+1-2 e^{3 x}}{x}\left[\frac{0}{0}\right] \\ = & \lim _{x \rightarrow 0} \frac{e^{x}-6 e^{3 x}}{1} \\ = & 1-6=-5\end{aligned} ==x→0limxex+1−2e3x[00]x→0lim1ex−6e3x1−6=−5
(Using La Hospital rule)
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=?
