Suppose y=arctan(2x) represents our happiness at in-comex, wherexis in hundreds of thousands of dollars (for example, x = 1means income = $100,000). Use differentials to estimate our change in happi-ness when we receive a raise of $10,000 in the following scenarios: our currentincome is a) $25,000, b) $50,000, c)$500,000. Hint: Use ∆x=dx, ∆y≈dy(change in happiness is ∆y).