Let f(x) = {((a(1 - xsinx) + bcosx + 5)/x^2, x < 0), (3, x = 0), ([1 + ((cx + dx^3)/x^2)]^1/x, x > 0).
Let f(x) = {((a(1 - xsinx) + bcosx + 5)/x2 x < 0) (3 x = 0) ([1 + ((cx + dx3)/x2)]1/x x > 0). If f is continuous at x = 0 then(A) a = -1(B) b = -4(C) c = 0(D) d = loge5
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The answer is (C). In order for f(x) to be continuous at x = 0, the left and right limits of f(x) must be equal at x = 0. This means that the limits of the two functions as x approaches 0 from the left and right should be the same (3). Since c is the only term in the function on the right side that is different than the function on the left side, c must be set to 0. So, c = 0.
