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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.
     Upload assignments properly through LMS, (No Assignment will be accepted through email).
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     This is not a group assignment, it is an individual assignment, so be careful and avoid copying othersí work. If any assignment is found to be copy of some other, both will be awarded ZERO MARKS. It also suggests you to keep your assignment safe from others. No excuse will be accepted by anyone if assignment is found to be copied or letting others to copy.

    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


    -5 -4 -3 -2 -1
    Question 2; Marks: 10
    Given two functions as:f(x) =
    x x
    − −
    and g(x) =3
    Find fog(x) also find the domain of
    )-3/x-1fog(x)= -(x
    (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
    x x x x

    − +−
    Lim(x->3) x(x
    -5x+6) / x
    Lim(x->3) x(x
    -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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