This problem deals with limits at infinity (and negative infinity) of certain exponential functions. X81 (a)...

 

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This problem deals with limits at infinity (and negative infinity) of certain exponential functions. X81 (a) Let f(x) = ex. Give a clear and convincing argument that lim f(x) = 0. This argument doesn't need to be very formal, but it should use the definition of ex to explain why the limit is zero. (b) Use the Sandwich Theorem (or, as it is sometimes known, the Squeeze Theorem) to show that lim 2e cos x = 0. x11 (c) Does the limit lim 2ex cos x exist? If so, what is its value? If not, does the function approach oo, 8118 -00, or neither? Justify your answer. This problem deals with limits at infinity (and negative infinity) of certain exponential functions. X81 (a) Let f(x) = ex. Give a clear and convincing argument that lim f(x) = 0. This argument doesn't need to be very formal, but it should use the definition of ex to explain why the limit is zero. (b) Use the Sandwich Theorem (or, as it is sometimes known, the Squeeze Theorem) to show that lim 2e cos x = 0. x11 (c) Does the limit lim 2ex cos x exist? If so, what is its value? If not, does the function approach oo, 8118 -00, or neither? Justify your answer.