A) 0
B) 1/2
C) 1
D) 2
Correct Answer: B
Solution :
\[\underset{x\to 1}{\mathop{\lim }}\,\frac{(1+\cos \pi x)}{{{\tan }^{2}}\pi x}=\underset{x\to 1}{\mathop{\lim }}\,\frac{-\pi \sin \pi x}{2\pi \tan \pi x{{\sec }^{2}}\pi x}\] [Using L-Hospital?s rule] \[=\underset{x\to 1}{\mathop{\lim }}\,\frac{-1}{2}{{\cos }^{3}}\pi \,x\]\[=\frac{1}{2}\].
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