MTH101 Calculus And Analytical Geometry Assignment No 1 Solution Fall 2012

Question # 01:                                                                                        05             

Find the equation for circle with center (1,3) that passes through (4, -1).

   

Sol.

 

Radius of circle r is the distance between (4, -1) and (1, 3)

 

 

Question # 02:                                                                                        05

Given that . Find . Also find the domains of the composite functions. 

Sol.

 

fog(x) = f ( g(x) )

            

             =  ( g(x) )2 – 4

            

              =  x-2- 4

              =  x-6

 

gof(x) =  g( f(x) )

Question # 03:                                                                                        05

Find . (Use rationalization technique to simplify)

Hint: (How to rationalize)

Rationalize the numerator of the expression .

Step I: find the conjugate of the numerator which is and vice versa.

Step II: multiply  the numerator and the denominator of the expression with the conjugate

Step III: make sure all the radicals are simplified

Step IV: simplify the fraction if needed.

In the same manner we can rationalize denominator too.

Sol. 

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