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Question Number 211873 by Spillover last updated on 22/Sep/24

Answered by IbtisamAdnan last updated on 23/Sep/24

$${\mathbf{lim}}_{\mathbf{x}\to 4}\frac{{\left(\mathbf{cos}\mathit{\alpha }\right)}^{\mathrm{x}}-{\left(\sin \alpha \right)}^{\mathrm{x}}-\cos 2\alpha }{\mathrm{x}-4}$$$${\mathbf{lim}}_{\mathbf{x}\to 4}\frac{{\left(\mathbf{cos}\mathit{\alpha }\right)}^{\mathrm{x}}.\ln \cos \alpha -{\left(\sin \alpha \right)}^{\mathrm{x}}.\ln \sin \alpha }{1}\left[\mathrm{L}\mathrm{hospital}\mathrm{rule}\right]$$$$=\left(\cos {}^4\alpha \right)\log \left(\cos \alpha \right)-{\left(\sin \alpha \right)}^4\log \left(\sin \alpha \right)$$$$\mathrm{Answer}\mathrm{is}\mathrm{b}$$

Commented by Spillover last updated on 23/Sep/24

$$correct.thanks$$

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