What is \lim_{x\rightarrow\frac{\pi}{2}}\frac{4x-2\pi}{\cos x} equal to ?
- A. -4 ✓
- B. -2
- C. 2
- D. 4
Correct Answer: A. -4
Explanation
The limit is in the \frac{0}{0} indeterminate form. Applying L'Hopital's rule, we differentiate the numerator and denominator to get \lim_{x\rightarrow\frac{\pi}{2}} \frac{4}{-\sin x}. Substituting x = \frac{\pi}{2} gives \frac{4}{-1} = -4.
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