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Question Number 134171 by liberty last updated on 28/Feb/21

$$\underset{x\to 0}{\lim }\frac{1+\sin \mathrm{x}-\cos \mathrm{x}}{1+\sin \left(\mathrm{px}\right)-\cos \left(\mathrm{px}\right)}=?$$

Answered by malwan last updated on 28/Feb/21

$$\underset{x\to 0}{lim}\frac{1+(x-...)-(1-...)}{1+(px-...)-(1-...)}=\frac{1}{p}$$

Answered by physicstutes last updated on 28/Feb/21

$$L=\underset{x\to 0}{\lim }\left(\frac{\cos x+\sin x}{p\cos px+p\sin px}\right)=\frac{1}{p}$$

Answered by liberty last updated on 01/Mar/21

$$\underset{x\to 0}{\lim }\frac{2\sin {}^2\left(\frac{1}{2}\mathrm{x}\right)+2\sin \left(\frac{1}{2}\mathrm{x}\right)\cos \left(\frac{1}{2}\mathrm{x}\right)}{2\sin {}^2\left(\frac{1}{2}\mathrm{px}\right)+2\sin \left(\frac{1}{2}\mathrm{px}\right)\cos \left(\frac{1}{2}\mathrm{px}\right)}$$$$=\underset{x\to 0}{\lim }\left[\frac{\sin \frac{1}{2}\mathrm{x}}{\sin \frac{1}{2}\mathrm{px}}\right].\underset{x\to 0}{\lim }\left[\frac{\sin \frac{1}{2}\mathrm{x}+\cos \frac{1}{2}\mathrm{x}}{\sin \frac{1}{2}\mathrm{px}+\cos \frac{1}{2}\mathrm{px}}\right]$$$$=\frac{1}{\mathrm{p}}\times 1=\frac{1}{\mathrm{p}}$$

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