The value of limx→π221cos2x+31cos2x+41cos2x+51cos2x+61cos2x2cos2x

limx→π2(2(1cos2x)+3(1cos2x)+4(1cos2x)+5(1cos2x)+6(1cos2x))2cos2xlimx→π2(61cos2x)2cos2x(26(1cos2x)+36(1cos2x)+46(1cos2x)+56(1cos2x)+1)2cos2x(61cos2x)2cos2x=62=36

The value of limx→π221cos2x+31cos2x+41cos2x+51cos2x+61cos2x2cos2x

limx→π2(2(1cos2x)+3(1cos2x)+4(1cos2x)+5(1cos2x)+6(1cos2x))2cos2xlimx→π2(61cos2x)2cos2x(26(1cos2x)+36(1cos2x)+46(1cos2x)+56(1cos2x)+1)2cos2x(61cos2x)2cos2x=62=36

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The value of $\lim_{x \to \frac{π}{2}} {(2^{\frac{1}{\cos^{2} x}} + 3^{\frac{1}{\cos^{2} x}} + 4^{\frac{1}{\cos^{2} x}} + 5^{\frac{1}{\cos^{2} x}} + 6^{\frac{1}{\cos^{2} x}})}^{2 \cos^{2} x}$

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$\frac{1}{36}$

answer is C.

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Detailed Solution

$\lim_{x \to \frac{π}{2}} {(2^{(\frac{1}{\cos^{2} x})} + 3^{(\frac{1}{\cos^{2} x})} + 4^{(\frac{1}{\cos^{2} x})} + 5^{(\frac{1}{\cos^{2} x})} + 6^{(\frac{1}{\cos^{2} x})})}^{2 \cos^{2} x}$

$\lim_{x \to \frac{π}{2}} {{(6^{\frac{1}{\cos^{2} x}})}^{2 \cos^{2} x} ({\frac{2}{6}}^{(\frac{1}{\cos^{2} x})} + {\frac{3}{6}}^{(\frac{1}{\cos^{2} x})} + {\frac{4}{6}}^{(\frac{1}{\cos^{2} x})} + {\frac{5}{6}}^{(\frac{1}{\cos^{2} x})} + 1)}^{2 \cos^{2} x}$