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Functions and Their Applications in Mathematics

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Added on  2021-01-01

Functions and Their Applications in Mathematics

   Added on 2021-01-01

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Functions and their applications
Functions and Their Applications in Mathematics_1
Table of ContentsQuestion 1: Completely factorize the following expressions:....................................................3Question 2: Find the following limits ??.....................................................................................4Question : 3 "A boat can travel at 32 km=hr in still water. It travels on a river, going 150kmupstream against the current, then returns to its starting location. Given that the boat istravailing at maximum speed the whole way, the total trip time is 10hr": What is the speed ofthe current, c? (in km=hr)............................................................................................................5Question : 4 sketches the curve of rational functions.................................................................6question : 5 Bonus questions: A rational functions.....................................................................8
Functions and Their Applications in Mathematics_2
Question 1: Completely factorize the following expressions:(a). 4 x^3+4 x^2-11 x-6=0Ans: (x+2)(2 x+1)(2 x-3)=>use the rational theorem=>a_0= 6, a_n= 4=> the dividers of a_0: 1,2,3,6. The dividers of a_n : 1,2,4Compute 4 x^3+4 x^2-11 x-6/ x+2 to get the rest of eqn- 4 x^2-4 x-3=> (x+2)(4 x^2-4 x-3)factors: (4 x^2-4 x-3)= (2 x+1)(2 x-3)=> (x+2)(2x+1)(2x-3)=0Using zero factor principle:x+2=0, x=-2x+2=0Case 1: Subtract both side 2x+2-2=0-2x=-2Solve 2x+1=0, x=-1/22x+1=0Case 2: subtract 1 both side2x+1-1=0-1simplify 2x=-1divide both side 22x/2=-1/2x=-1/2Case 3: 2x-3=0, x=3/22x-3=0Add 3 in both side2x-3+3=0+3simplify2x=3divide both sides by 2
Functions and Their Applications in Mathematics_3

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