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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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Limit x tends to a (sin x-sin a)/(x-a)|$\lim_{x\rightarrow a}\frac{\sin x – sina}{x – a}$ -This is an Important Mathematical Problem of Limit Chapter fo Class 11 of Some Important Books of CBSE, ISC, WBCHSE, RD Sharma, NCERT, JEE, Etc.

Limit x tends to a (sin x-sin a)/(x-a)

$\lim_{x\rightarrow a}\frac{\sin x – sina}{x – a}$
= $\lim_{x\rightarrow a}\frac{2cos\frac{x + a}{2}\sin \frac{x – a}{2}}{2.\frac{x – a}{2}}$
= $\lim_{x\rightarrow a}\frac{\sin \frac{x – a}{2}}{\frac{x – a}{2}}\ldotp \lim_{x\rightarrow a}cos\frac{x + a}{2}$
= $\lim_{z\rightarrow 0}\frac{\sin \frac{z}{2}}{\frac{z}{2}}\ldotp \lim_{x\rightarrow a}cos\frac{x + a}{2}$
[Let x – a = z and x $\rightarrow a$$\Rightarrow z$$\rightarrow 0$]
= $1.cos\frac{a + a}{2}$
= cosa

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 h tends to zero $\lim_{h\rightarrow 0}\frac{1 – cosh}{hsinh}$

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