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  • What is the value of <img alt="\lim _{x \rightarrow 0} \frac{\cos a x-\cos b x}{x^{2}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Clim%20_%7Bx%20%5Crightarrow%200%7D%20%5Cfrac%7B%

What is the value of \lim _{x \rightarrow 0} \frac{\cos a x-\cos b x}{x^{2}}

Option: 1

{\frac{a^{2}-b^{2}}{2}}


Option: 2

{\frac{b^{2}-a^{2}}{2}}


Option: 3

{a^{2}-b^{2}}


Option: 4

{b^{2}-a^{2}}


Answers (1)

best_answer

\\\text{As we know }\\\\ \cos x=1-\frac{x^{2}}{2 !}+\frac{x^{4}}{4 !}-\ldots \ldots \\\\So,\,\, \lim _{x \rightarrow 0} \frac{\cos a x-\cos b x}{x^{2}}\\=\lim _{x \rightarrow 0} \frac{[1-\frac{(ax)^{2}}{2 !}+\frac{(ax)^{4}}{4 !}- \cdots]-[1-\frac{(bx)^{2}}{2 !}+\frac{(bx)^{4}}{4 !}- \cdots ]}{x^{2}}\\\\ =\frac{b^2-a^2}{2}

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vishal kumar

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