Contaminated limits

Calculus Level 2

lim ⁡ x → 0 tan ⁡ ( x ) − x x 3 = ? \large \displaystyle\lim_{x \rightarrow 0} \displaystyle\frac{\tan( x) - x}{x^{3}} = \ ?

1 3 \frac{1}{3} 1 2 \frac{1}{2} 1 4 \frac{1}{4} 2 3 \frac{2}{3}

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Samuel Ayinde by samuel ayinde , 24, Nigeria

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3 solutions

Raushan Sharma
Sep 14, 2015

Just use L-Hospital's Rule. Here, we need to do the 2nd derivative, if we use L-Hospital's rule

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Saurabh Patil
Apr 14, 2015

Use the following expansion of tan x

1/3 would be the required answer.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Samuel Ayinde
Sep 14, 2015

Nice solutions!!!!

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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