Recall the definition of O(.) notation (a) It turns out that 400x + 9000x=0(x). Please prove...

  

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Recall the definition of O(.) notation (a) It turns out that 400x³ + 9000x²=0(x³). Please prove this, i.e., find constants C, M>0 such that 400x3³ +9000x² <Mr³ for all x>C. x (b) It turns 500x³ <e for x sufficiently large. How large is large enough? Please prove your answer. (c) It turns out that e20√√log x < ex for x sufficiently large. How large is large enough? Please prove your answer. (d) It turns out that e40x1/3 (log x)2/3 enough? Please prove your answer. <e√√log for all x sufficiently large. How large is large Recall the definition of O(.) notation (a) It turns out that 400x³ + 9000x²=0(x³). Please prove this, i.e., find constants C, M>0 such that 400x3³ +9000x² <Mr³ for all x>C. x (b) It turns 500x³ <e for x sufficiently large. How large is large enough? Please prove your answer. (c) It turns out that e20√√log x < ex for x sufficiently large. How large is large enough? Please prove your answer. (d) It turns out that e40x1/3 (log x)2/3 enough? Please prove your answer. <e√√log for all x sufficiently large. How large is large