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please help me in solve these...............................................................

please help me in solve these...............................................................

Question Image
Grade:12

1 Answers

ajay sangh
29 Points
3 years ago
in your first question on finding the maximum value of “e” to the power of some function,that function is unclear please post it clearly. and the second goes this way,the question says that integrate that function whose value is maximum,so, \int_{0}^{\pi }max(cosx,sinx)=\int_{0}^{\frac{\pi }{4}}cosx+\int_{\frac{\pi }{4}}^{\pi }sinxnow in the third question,\sum_{1}^{100}\frac{1}{4n^{2}-1}=\sum_{1}^{100}\frac{1}{(2n-1)(2n+1)}=\frac{1}{2}(\sum_{1}^{100}\frac{1}{2n-1}-\sum_{1}^{100}\frac{1}{2n+1})=\frac{1}{2}(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}........\frac{1}{199}-\frac{1}{201})=\frac{1}{2}(1-\frac{1}{201})=\frac{100}{201}

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