Points Find a simple function g of the smallest order so...

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MAT 243 Week 4/7 Written Homework 1. (4 points) Find a simple function g of the smallest order so that f ( x ) is big-O of g ( x ). In your estimation you can use theorems learned in lecture about the big-O estimates of sums/products of functions. f ( x ) = ( x 2 . 3 + x ln x 5 )(1 . 1 x +1 + 1 . 2 x ) + ( x 2 + 1 . 2 x )( x 3 + 0 . 92 x ) 2. (4 points) Is there a smallest real number a for which x 2 6 x is big-O of a x ? Explain your answer. 3. (1 point) Carry out the hexadecimal addition CA10 + 4F57 directly in hexadecimal. Do not convert the numbers to decimal, add them in deci- mal and convert the sum back to hexadecimal. 4. (1 point) Carry out the binary multiplication 11011 times 1001 using only left bit shifts and addition. 5. (4 points) Use the Euclidean Algorithm to demonstrate that 621 and 82 are relatively prime to each other. Explain. 6. (4 points) Given an integer n , show that you can multiply n by 35 us- ing only five multiplications by 2, two additions and storing intermediate

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