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Example 30 The value of k which makes the function defined by, , a, ifx#0, , s, f=) x , continuous at x=0 is, kk, ifx=0, (A) 8 ®) 1, (Cr -1 () _ noneof these, , - ., Solution (D) is the correct answer. Indeed tim sin— does not exist., 90 x, , Example 31 The set of points where the functions f given by f (x) = |x — 3| cosx is, differentiable is, , CONTINUITY AND DIFFERENTIABILITY — 105, , (A) R (B) R- {3}, , (©) @,~) (D) none of these, Solution B is the correct answer., Example 32 Differential coefficient of sec (tan“'x) w.r-t. x is, , , , , , (A) (B), , +x?, , , , © xfer leer, , Solution (A) is the correct answer., , , , 2x 2x d, , = a 4 lu, = sin = tan'] —} &, , Example 33 Ifu= ( e Jon v= ( ee } then is, , , , (A) 2 (B) ox (©) Tat, , Solution (D) is the correct answer., Example 34 The value of c in Rolle’s Theorem for the function f (x) = e* sinx,, xe[0,m]is, , A Bw (©), , Solution (D) is the correct answer., , Example 35 The value of c in Mean value theorem for the function f (x) = x (x - 2),, xe [1,2] is, , ec, 2, , Ag (B) 3 (©) 3 O 3, , Solution (A) is the correct answer., Example 36 Match the following, , COLUMN-I COLUMN-II, sin3x itxe0, (A) Ifafunction (x)= % (a) bl, 5 ifx=0, , is continuous at x = 0, then k is equal to