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Given \( f(x)=(a-11) \tan x+(b-3) \ln x+(c-4) e^{x}+\sin x \) value of \( a+b+c \) for which \( f(x) \) is a bounded function. |
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Answer» Given function is f(x) = (a - 11) tan x + (b - 3) lnx + (c - 4)ex + sin x \(\because\) tan x, ln x and ex is unbounded function and sin x is a bounded function. Given that f(x) is bounded function which is possible only when there is no term of tan x, ln x and ex in f(x). \(\therefore\) f(x) is bounded if a - 11 = 0, b - 3 = 0 and c - 4 = 0 or a = 11, b = 3 and c = 4 \(\therefore\) a + b + c = 11 + 3 + 4 = 18 Hence, a + b + c = 18 for which given function is bounded. |
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