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Thread: MTH 101 Calculus And Analytical Geometry Assignment No.1 Spring April 10 2012

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    Icon51 MTH 101 Calculus And Analytical Geometry Assignment No.1 Spring April 10 2012

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    MTH 101 Calculus And Analytical Geometry Assignment No.1 Spring April 10 2012

    Assignment No. 1
    MTH 101 (Spring 2012)


    Maximum Marks: 20
    Due Date: 18th April. 2012

    DONíT MISS THESE Important instructions:

     To solve this assignment, you should have good command over first
    08 lectures.
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    Question # 01: 10
    Solve the following inequalities.






    Question # 02: 10
    Given that . Find . Also, find the domains of composite functions.




    (Note: In order to get full marks, do all necessary steps)


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    Idea Solution


    Solve the two sided inequality and show the solution on real line7 < 1-2x ≤ 10Step 1: subtract 1 from both sides and we get6<-2x<9Step2: divide by -2 on both sides and we get-3>x>-5(note: symbols are reversed with a negative operation)So x can have a value between -3 and or equal to -5


    --
    |---|-----
    |
    -----|----|---0--------------------------------

    -5 -4 -3 -2 -1
    Question 2; Marks: 10
    Given two functions as:f(x) =
    2
    1
    x x
    − −
    and g(x) =3
    x
    Find fog(x) also find the domain of
    f
    ,
    g
    and
    fogSolution:
    Fog(x)=f(g(x))fog(x)=(g(x))
    2
    -(g(x))-1fog(x)=(3/x)
    2
    -(3/x)-1fog(x)=(9/x
    2
    )-3/x-1fog(x)= -(x
    2
    -3x+9)/x
    2
    (note: domain and ranges are to be found out yourselves, listen to lecture No. 6 for this)
    Question 3; Marks:10
    Simplify, then apply the rules of limit to evaluate
    3 232
    56lim9
    x
    x x x x

    − +−
    Solution:
    Lim(x->3) x(x
    2
    -5x+6) / x
    2
    -3
    2
    Lim(x->3) x(x
    2
    -3x-2x+6) / (x-3)(x+3)Lim(x->3) x(x(x-3)-2(x-3)) / (x-3)(x+3)Lim(x->3) x((x-3)(x-2)) / (x-3)(x+3)Lim(x->3) x(x-2) /(x+3) Now applying limits lim x->3=3(3-2)/3+3=3(1)/6=3/6=Ĺ


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