Find the limit.
A) 0
B) 1
C) -1
D) +$\infty$
E) -$\infty$

Name: Find the limit. A) 0 B) 1 C) -1 D) +$\infty$ E) -$\infty$
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Question

Find the limit. 
A) 0 
B) 1 
C) -1 
D) +$\infty$ 
E) -$\infty$

Quizplus · Accepted Answer

The given limit is indeterminate, so we can apply L'Hopital's rule. Taking the derivative of the numerator and denominator with respect to x, we get:
lim x->0 ((2x)/(1+x^2))/(x*cos(x))
= lim x->0 (2*(1+x^2)-2x^2)/(1+x^2)^2 * 1/(cos(x)-x*sin(x))
= lim x->0 (4x)/(2x*cos(x)-x^2*sin(x)+1+x^2)^2
= 0/1 = 0
Therefore, the limit is 0.

Find the Limit ∞\infty∞ E) - ∞\infty∞

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