আমাদের টেলিগ্রাম চ্যানেলে যুক্ত হোন

Evaluate: Limit x tends to zero (cosx-secx)/x^2||$\lim_{x\rightarrow 0}\frac{\cos x – secx}{x^2}$

by

Evaluate: $\lim_{x\rightarrow 0}\frac{\cos x – secx}{x^2}$

$\lim_{x\rightarrow 0}\frac{\cos x – secx}{x^2}$
= $\lim_{x\rightarrow 0}\frac{\cos x – \frac{1}{\cos x}}{x^2}$
= $\lim_{x\rightarrow 0}\frac{\cos^2x – 1}{x^2\cos x}$
= $\lim_{x\rightarrow 0}\frac{ – sin^2x}{x^2cosx}$
= $- \left(\lim_{x\rightarrow 0}\frac{\sin x}{x}\right)^2\lim_{x\rightarrow 0}\frac{1}{\cos x}$
=$ – (1)^2\ldotp 1$
= – 1

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 $\lim_{x\rightarrow 0}\frac{1 – cosx}{\sin^2x}$
  4. Limit x Tends to Zero $\lim_{x\rightarrow 0}\frac{xtanx}{1 – cosx}$
  5. Evaluate: $\lim_{x\rightarrow 0}\frac{1 – cos2x}{3tan^2x}$

Leave a Comment

error: Content is protected !!