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Match the conditions/ expressions in Column I with statements in Column II. Let the functions defined in Column I have domain ` (-pi//2, pi//2)`. |
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Answer» `(d)/(dx) ( x + sin x ) = 1 + cos x = 2 cos ^(2)""(x)/(2) gt 0 "for " - (pi)/(2) lt x lt (pi)/(2)`. Therefore , ` x + sin x ` is increasing in the given interval. Therefore, `(A) to (p)` is the answer. Again `(d)/(dx) (sec)= secx tanx ` which is ` gt 0 " for " 0 lt x lt pi//2 ` and `" " lt 0 " for " (-pi)/(2) lt x lt 0` Therefore, `sec x ` is neither increasing nor decreasing in the given interval. Therefore, `(B) to (r) ` is the answer. |
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