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Please answer the following problems using COMPLETE and GRAMMATICALLY CORRECT sentences. Please provide all supporting work...

Please answer the following problems using COMPLETE and GRAMMATICALLY CORRECT sentences. Please provide all supporting work for your solution..

1. Show that f ( x ) = a x grows faster than g ( x ) = b x as x ⟶ ∞ if 1 < b < a.

2. Show that f ( x ) = x x grows faster than g ( x ) = b x as x ⟶ ∞ if b > 1.

3. Prove that lim x ⟶ ∞ ( 1 + a x ) x = e a for a ≠ 0.

Math   Calculus   
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