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answerhappygod
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T/F?
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1. The radius of convergence of a power series is either 0,1 or ∞. If f(x)=n=0∑∞anxn for all x, then f′(x)=n=1∑∞nanxn−1 for all x. 3. If f(x)=n=0∑∞anxn for all x, then ∫f(x)dx=C+n=0∑∞ann+1xn+1 for all x. 4. If R>0 and f(x)=n=0∑∞anxn for all x∈(−R,R), then an=n!f(n)(0) for all n.
1. The radius of convergence of a power series is either 0,1 or ∞. If f(x)=n=0∑∞anxn for all x, then f′(x)=n=1∑∞nanxn−1 for all x. 3. If f(x)=n=0∑∞anxn for all x, then ∫f(x)dx=C+n=0∑∞ann+1xn+1 for all x. 4. If R>0 and f(x)=n=0∑∞anxn for all x∈(−R,R), then an=n!f(n)(0) for all n.
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