question archive Suppose that f(x) is a continuous function on the interval [0,pi]
Suppose that f(x) is a continuous function on the interval [0,pi]
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Suppose that f(x) is a continuous function on the interval [0,pi]. if f(x) = (sinx)x for (0,pi], then what is f(0)
a) e
b) 0
c) e-1
d) -1
e) 1
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Since the f(x) is continuous function in [0, π], therefore the value of function at x = 0 must equal to its right hand limit.
i.e, f(0) = limx->0+ f(x) = limx->0+ (sin x)x
Using the method to calculate the limit, the result is:
f(0) = limx->0+ (sin x)x = 1
Answer: (e) 1
