আমাদের টেলিগ্রাম চ্যানেলে যুক্ত হোন

Evaluate: $\lim_{x\rightarrow 0}\frac{1 – cos2x}{3tan^2x}$

by

Limit x Tends to Zero (1-cos2x)/3 tan^2x

$\lim_{x\rightarrow 0}\frac{1 – cos2x}{3tan^2x}$
= $\lim_{x\rightarrow 0}\frac{\cos^2x + sin^2x – (cos^2x – sin^2x)}{3tan^2x}$
= $\lim_{x\rightarrow 0}\frac{\cos^2x + sin^2x – cos^2x + sin^2x}{3tan^2x}$
= $\lim_{x\rightarrow 0}\frac{2sin^2x}{3tan^2x}$
= $\lim_{x\rightarrow 0}\frac{2sin^2x}{3\frac{\sin^2x}{\cos^2x}}$
=$ \lim_{x\rightarrow 0}\frac{2sin^2xcos^2x}{3sin^2x}$
= $\frac{2}{3}\lim_{x\rightarrow 0}\cos^2x $
= $\frac{2}{3}$

আরও দেখুন

  1. Evaluate: $\lim_{x\rightarrow 0}\frac{\sin x(1 – cosx)}{x^3} $
  2. Limit x Tends to Zero $\lim_{x\rightarrow 0}\frac{1 – cosx}{x^2}$
  3. Limit X Tends to Zero $\lim_{x\rightarrow 0}\frac{1 – cos4x}{x^2}$
  4. Limit h Tends to 0 $\lim_{h\rightarrow 0}\frac{\cos ah – cosbh}{h^2}$
  5. Limit x Tends to Zero $\lim_{x\rightarrow 0}\frac{1 – cosx}{\sin^2x}$

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