a) Computing values of f near x=0, we discover that f(0.1)=0.1, f(0.01)= 0.01, f(0.001)=0.001, f(0.0001)=0.0001, and...

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a) Computing values of f near x=0, we discover that f(0.1)=0.1, f(0.01)= 0.01, f(0.001)=0.001, f(0.0001)=0.0001, and f(0.00001)=0.00001. Can we conclude that lim f(x)=0? b) For all values of k #0, you discover that f(3+k) lies between 5 and 5+k². Can you conclude that lim f(x)=5?. Either give a counter-example or explain which x 3 theorem guarantees this conclusion. a) Computing values of f near x=0, we discover that f(0.1)=0.1, f(0.01)= 0.01, f(0.001)=0.001, f(0.0001)=0.0001, and f(0.00001)=0.00001. Can we conclude that lim f(x)=0? b) For all values of k #0, you discover that f(3+k) lies between 5 and 5+k². Can you conclude that lim f(x)=5?. Either give a counter-example or explain which x 3 theorem guarantees this conclusion.

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a We see that as the value of x approaches near 0 the value of the functi... View the full answer