MTH 101 Calculus And Analytical Geometry Assignment No.1 Fall Semester 2012

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MTH 101 Calculus And Analytical Geometry Assignment No.1 Fall Semester 2012


Assignment No. 1
MTH 101 (Fall 2012)

Maximum Marks: 15
Due Date: 12th Nov. 2012

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Question # 01: 05

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

Question # 02: 05

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

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.

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

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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)

Sol.



When we apply limit as put x= 0 our answer will be 0