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Assignment No. 1
MTH 101 (Fall 2012)
Maximum Marks: 15
Due Date: 12^{th} Nov. 2012
DON’T MISS THESE Important instructions:
10 lectures.
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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One more
MTH101 Current Assignment Solution No.1 Fall 2012
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) )
Calculus And Analytical Geometry assignment solution.
Calculus And Analytical Geometry assignment solution.
Question # 01:
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:
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:
Find . (Use rationalization technique to simplify)
dear how to write symbols like underroot in Ms word??
Download the program Math Type or Arithmetic Expression.
Squroot ka domain hai 1 or -6 infinity abe dono ka unione ley loo. (- infinity ,+ infinity)U(1, - infinity)
(1, - infinity ) jawab hai , ap key sewal kei mutabiq, ager value change hai to jawab per dosra hoga.
what is the final domain you got of Q.2? and also tell me is the part 2 of a question possess composite function?
plz uplaod the complete solution. I'm facing some prb in Q.2. I've done it bt I'm not sure I did right
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) )
Anything in a square root cannot be negative because it would be undefined. And the denominator in a fraction cannot be zero
So the domain is where x/(x-6) ≥ 0 and where x - 6 ≠ 0
So then x ≥ 0 and x ≠ 6
So the domain would be: 0 ≤ x < 6 and 6 < x < ∞
It can also be written this way: [0,6) and (6,∞)
The domain is the x the range is the y. The domain is an independent variable because it is not influenced by anything. The y is dependent because it is influenced by the independent variable.
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