Expert: Ahmed Salami - 2/25/2010

Question
Lim (4x-3)/(2x+7)       (Where  x tend to INFINITY)

Solution:
Lim ( (4x/2x)-(3/2x))/((2x/2x)+(7/2x)         (where x tends to INFINITY)
Lim (2+0)/(1+0)=2                                          (where   x tends to INFINITY)

Sir  I understand this problem .but a question arise in my mind that is why they have divide the  both numerator and denominator by 2x.please reply me sir

Answer
Hi Pratap,
Its a good trick to divide numerator and denominator by the highest occuring power of the variable, which in this case is x. This ensures that we have terms in 1/x and we know that 1/x tends to zero as x tends to infinity, making the limit easier to determine.

Regards