MathDB
CMI's Integral function

Source: CMI 2024

May 19, 2024
calculusintegrationfunction

Problem Statement

g(x) ⁣:∫10xlog⁡10(log⁡10(t2−1000t+101000))dtg(x) \colon \int_{10}^{x} \log_{10}(\log_{10}(t^2-1000t+10^{1000})) dt
(a) Find the domain of g(x)g(x) (b) Approximate the value of g(1000)g(1000) (c) Find x∈[10,1000]x \in [10, 1000] to maximize the slope of g(x)g(x) (d) Find x∈[10,1000]x \in [10, 1000] to minimize the slope of g(x)g(x) (e) Determine, if it exists, lim⁡x→∞ln⁡(x)g(x)\lim_{x \to \infty} \frac{\ln(x)}{g(x)}
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