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| 1. |
find derivative of sin x by first principle.\xa0 |
| Answer» The derivative of sin(x) from first principles.Setting aside the limit for now, our first step is to evaluate the fraction with\xa0f(x) = sin\xa0x.On the right hand side we have a difference of 2 sines, so we apply the formula in (A2) above:Simplifying the right hand side gives:Now to put it all together and consider the limit:We make use of (3), fraction on a fraction, to bring that 2 out front down to the bottom:Now, the limit of a product is the product of the limits, so we can write this as:\xa0Now, the first limit is in the form of\xa0Limit of sin θ/θ\xa0that we met in (A1) above.We know it has value 1.For the right hand limit, we simply obtain cos\xa0x.So we can conclude that | |