Thank you Pi Han!

Calculus Level 2

Evaluate

$\large\lim_{x\rightarrow 1729} \displaystyle \dfrac{314x^2-31.4x+3.14}{x-1729}$

This problem is original

2957.86 Not defined 2958.86 1536.86

2 solutions

Nihar Mahajan
Oct 25, 2015

Note that the denominator becomes $0$ and if the numerator is also $0$ , then only the limit can be evaluated. So let's check the discriminant of the the numerator: $314x^2-31.4x^2+3.14$

$\Delta = (31.4)^2-4(314)(3.14) \approx 31^2-4(314)(3) \approx 961-4(942) < 0$

Thus the expression $314x^2-31.4x^2+3.14>0$ , hence , limit does not exist.

Moderator note:

Always remember the conditions of a theorem before attempting to apply it.

In response to challenge master:

In this case the L'Hôpital's Rule .

Tapas Mazumdar - 4 years, 2 months ago

Atul Shivam
Oct 29, 2015

Numerator is non zero whereas denominator is zero hence limit doesn't exist in this case

Thank you Pi Han!

This problem is original

2 solutions

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