Division requires a larger computational budget than multiplication (computers are just like us, we hate long division!), which can cause issues in responsiveness of user interfaces, framerates in videogames, and the time needed to run simulations for important engineering problems. (a) Find the linearization, L(x), of f(x) = for x near 1. (b) It can often save significant time to use the above linearization to approximate x с ≈ CL(x), x since multiplication is computationally cheaper than division. For numbers x ≈ 1 the loss in accuracy is negligible compared to the gain in efficiency.

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A:

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