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Limit x Tends to 0 cosec x-cot x/x|$\lim_{x\rightarrow 0}\frac{\cos ecx – cotx}{x}$

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Limit x Tends to 0 cosec x-cot x/x | $\lim_{x\rightarrow 0}\frac{\cos ecx – cotx}{x}$-This is an Important Sum of Limit Chapter of Class 11 of Some Important Math Books like SN Dey, RD Sharma, NCERT, CBSE, ISC, JEE, WBCHSE, Etc.

Limit x Tends to 0 cosec x-cot x/x

$\lim_{x\rightarrow 0}\frac{\cos ecx – cotx}{x}$
= $\lim_{x\rightarrow 0}\frac{\frac{1}{\sin x} – \frac{\cos x}{\sin x}}{x}$
= $\lim_{x\rightarrow 0}\frac{1 – cosx}{xsinx}$
= $\lim_{x\rightarrow 0}\frac{2sin^2\frac{x}{2}}{2xsin\frac{x}{2}\cos \frac{x}{2}}$
= $\lim_{x\rightarrow 0}\frac{\sin \frac{x}{2}}{x\cos \frac{x}{2}}$
= $\lim_{x\rightarrow 0}\frac{\sin \frac{x}{2}}{2.\frac{x}{2}}\ldotp \lim_{x\rightarrow 0}\frac{1}{\cos \frac{x}{2}}$
= $\frac{1}{2}\lim_{x\rightarrow 0}\frac{\sin \frac{x}{2}}{\frac{x}{2}}\ldotp \lim_{x\rightarrow 0}\frac{1}{\cos \frac{x}{2}} $
= $\frac{1}{2}$

আরও দেখুন

  1. Limit x Tends to Zero $\lim_{x\rightarrow 0}\frac{1 – cosx}{x^2}$
  2. Limit X Tends to Zero $\lim_{x\rightarrow 0}\frac{1 – cos4x}{x^2}$
  3. Limit h Tends to 0 $\lim_{h\rightarrow 0}\frac{\cos ah – cosbh}{h^2}$
  4. Limit x Tends to Zero $\lim_{x\rightarrow 0}\frac{1 – cosx}{\sin^2x}$
  5. Limit x tends to a (sin x-sin a)/(x-a)|$\lim_{x\rightarrow a}\frac{\sin x – sina}{x – a}$

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