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limx→2x3−8x2−4 \lim _{x \rightarrow 2} \frac{x^{3}-8}{x^{2}-4} limx→2x2−4x3−8
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limx→2x3−8x2−4=limx→23x2−02x−0 [L’Hopitals] =limx→23x22x=3.222⋅2=124=3 \begin{array}{l}\lim _{x \rightarrow 2} \frac{x^{3}-8}{x^{2}-4} \\ =\lim _{x \rightarrow 2} \frac{3 x^{2}-0}{2 x-0} \quad \text { [L'Hopitals] } \\ =\lim _{x \rightarrow 2} \frac{3 x^{2}}{2 x} \\ =\frac{3.2^{2}}{2 \cdot 2} \\ =\frac{12}{4}=3\end{array} limx→2x2−4x3−8=limx→22x−03x2−0 [L’Hopitals] =limx→22x3x2=2⋅23.22=412=3
If the function f(x)=(1−x)tanπx2f(x) = (1 - x)\tan \dfrac{{\pi x}}{2}f(x)=(1−x)tan2πx is continuous at x=1x = 1x=1 ,then f(1)=f(1)=f(1)=
limx→0xtan2x−2xtanx(1−cos2x)2 \displaystyle \lim _{x \rightarrow 0} \dfrac{x \tan 2 x-2 x \tan x}{(1-\cos 2 x)^{2}} x→0lim(1−cos2x)2xtan2x−2xtanx is equal to
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নিচের সীমার মান কোনটি? limx→ysinx−sinyx−y\lim _{x \rightarrow y} \frac{\sin x-\sin y}{x-y}limx→yx−ysinx−siny
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