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Limit h Tends to 0 $\lim_{h\rightarrow 0}\frac{\cos ah – cosbh}{h^2}$

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Limit h Tends to 0 $\lim_{h\rightarrow 0}\frac{\cos ah – cosbh}{h^2}$

$\lim_{h\rightarrow 0}\frac{\cos ah – cosbh}{h^2}$
= $\lim_{h\rightarrow 0}\frac{2sin\frac{ah + bh}{2}\sin \frac{bh – ah}{2}}{h^2}$
= $\lim_{h\rightarrow 0}\frac{2sin\frac{ah + bh}{2}\sin \frac{bh – ah}{2}}{h\ldotp h}$
= $\lim_{h\rightarrow 0}\frac{2sin\frac{ah + bh}{2}}{h}\ldotp \lim_{h\rightarrow 0}\frac{sin\frac{bh – ah}{2}}{h}$
= $\lim_{h\rightarrow 0}\frac{sin\frac{h(a + b)}{2}}{\frac{h(a + b)}{2}}(a + b)\ldotp \lim_{h\rightarrow 0}\frac{sin\frac{h(b – a)}{2}}{2.\frac{h(b – a)}{2}}(b – a)$
= $(b + a) \times \lim_{h\rightarrow 0}\frac{sin\frac{h(a + b)}{2}}{\frac{h(a + b)}{2}} \times \frac{(b – a)}{2} \times \lim_{h\rightarrow 0}\frac{sin\frac{h(b – a)}{2}}{2.\frac{h(b – a)}{2}}$
= $(b + a) \times \frac{(b – a)}{2}$
= $\frac{b^2 – a^2}{2}$

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 x Tends to Zero $\lim_{x\rightarrow 0}\frac{1 – cosx}{\sin^2x}$
  4. Limit h tends to zero $\lim_{h\rightarrow 0}\frac{1 – cosh}{hsinh}$
  5. Limit x Tends to Zero $\lim_{x\rightarrow 0}\frac{xtanx}{1 – cosx}$

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