Please answer the step 5 and step 6. Thank you!
Subject: Discrete Mathematics
Lesson: Big-O Notation
k. (a) Show that f(x) = x² + 2x + 1 is 0(x*) Solution: When x>1; x2 + < x?="" (1+="4x2" so,="" for="" x=""> 1,x2 + 2x +1< 4x?="" from="" the="" definition="" 0="" s="" f(x)="" s="" cg(x)="" for="" x21="" hence,="" for="" no="1;" c="4:" and="" g(x)="x2" for="" no="2;" c="3:" and="" g(x)="x2" for="" no="3;" c="2;" and="" g(x)="x?" therefore,="" x?="" +="" 2x+1="0(x2)" o(g(x))="{f(x)|there" exist="" positive="" constant="" c="" and="" no="" such="" that="" 0s="" f(x)="" s="" cg(x)="" for="" all="" x2no}="" 2.="" show="" that="" 7x2="" is="" o(x³).="" 3.="" suppose="" there="" are="" x="" number="" of="" boxes="" to="" be="" delivered="" to="" x="" number="" of="" household="" that="" is="" 2km="" apart,="" what="" is="" the="" distance="" travelled="" by="" the="" transport="" delivery="" service?="" "/="">
Extracted text: Learning Task 7- GROWTH OF FUNCTIONS 1. Big-O Notation Let fand g be functions from the set of integers or the set of real numbers to the set ofreal numbers. We say that f ( x) is 0 (g (x)), read as "f(x) is big-oh of g (x)", if there are constants C and k such that | f (x)|sCig(x)|whenever x>k. (a) Show that f(x) = x² + 2x + 1 is 0(x*) Solution: When x>1; x2 + < x?="" (1+="4x2" so,="" for="" x=""> 1,x2 + 2x +1< 4x?="" from="" the="" definition="" 0="" s="" f(x)="" s="" cg(x)="" for="" x21="" hence,="" for="" no="1;" c="4:" and="" g(x)="x2" for="" no="2;" c="3:" and="" g(x)="x2" for="" no="3;" c="2;" and="" g(x)="x?" therefore,="" x?="" +="" 2x+1="0(x2)" o(g(x))="{f(x)|there" exist="" positive="" constant="" c="" and="" no="" such="" that="" 0s="" f(x)="" s="" cg(x)="" for="" all="" x2no}="" 2.="" show="" that="" 7x2="" is="" o(x³).="" 3.="" suppose="" there="" are="" x="" number="" of="" boxes="" to="" be="" delivered="" to="" x="" number="" of="" household="" that="" is="" 2km="" apart,="" what="" is="" the="" distance="" travelled="" by="" the="" transport="" delivery="">
Extracted text: apait, 4. In number 3, suppose that each boxes must be coming from the Warehouse and the transport delivery service must need to back-and-port to pick-up each box. What is the distance travelled by the transport delivery service? 5. Evaluate the methods used in number 3 and number 4 method of delivery. If the function x2 is considered as the dominant term for each method used. 6. What will happen to the term 2x + 5 of the original function x? + 2x + 5 when compared to the dominant term which is x?. Show a simple analysis for this function.