Ordering Limits of Indeterminate Forms

Question

Evaluate the following limits that initially present indeterminate forms and rank their values in increasing order:
(i) $$\lim_{x	o0}\frac{1-\cos(x)}{x^2} = \frac{1}{2}$$,
(ii) $$\lim_{x	o0}\frac{e^{x}-1}{x} = 1$$,
(iii) $$\lim_{x	o0}\frac{\sin(2*x)}{x} = 2$$,
(iv) $$\lim_{x	o0}\frac{\ln(1+3*x)}{x} = 3$$.
Rank these limits from smallest to largest.

Accepted Answer

1-cos(x)/x^2, (e^x-1)/x, sin(2*x)/x, ln(1+3*x)/x

Answer

sin(2*x)/x, 1-cos(x)/x^2, ln(1+3*x)/x, (e^x-1)/x

Answer

(e^x-1)/x, 1-cos(x)/x^2, sin(2*x)/x, ln(1+3*x)/x

Answer

ln(1+3*x)/x, sin(2*x)/x, (e^x-1)/x, 1-cos(x)/x^2

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