(Step-by-Step) Let f(x):=x^2 sin (1 / x) for x ≠q 0, let f(0):=0, and let g(x):= sin x for x ∈ R. Show that lim _x \rightarrow 0 f(x) / g(x)=0 but that
Question: Let \(f(x):=x^{2} \sin (1 / x)\) for \(x \neq 0\), let \(f(0):=0\), and let \(g(x):=\sin x\) for \(x \in \mathbb{R}\). Show that \(\lim _{x \rightarrow 0} f(x) / g(x)=0\) but that \(\lim _{x \rightarrow 0} f^{\prime}(x) / g^{\prime}(x)\) does not exist.
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![[Step-by-Step] Show that if a > 0,](/images/solutions/MC-solution-library-31090.jpg "[Step-by-Step] Show that if a > 0, then the convergence of the")
[Step-by-Step] Show that if a > 0, then the convergence of the
(Step-by-Step) Show that if x>0, then 1+1/2 x-1/8 x^2 ≤q √1+x
![[Solved] If f(x):=e^x, show that the remainder](/images/solutions/MC-solution-library-31092.jpg "[Solved] If f(x):=e^x, show that the remainder term in Taylor's")
[Solved] If f(x):=e^x, show that the remainder term in Taylor's
![[Solution Library] If g(x):= sin x, show](/images/solutions/MC-solution-library-31093.jpg "[Solution Library] If g(x):= sin x, show that the remainder term in Taylor's")
[Solution Library] If g(x):= sin x, show that the remainder term in Taylor's
![[See Steps] Show that the function f(x):=1](/images/solutions/MC-solution-library-31094.jpg "[See Steps] Show that the function f(x):=1 / x^2 is uniformly")
[See Steps] Show that the function f(x):=1 / x^2 is uniformly
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