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If fx=1+sinx-1-sinxx, x0 is continuous at x=0, then f0 is

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Important Questions on Continuity

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If the function fx=cos2x-sin2x-1x2+1-1, x0 is continuous at x=0, then f0 is equal to
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The value of f at x=0, so that the function fx=2x-2-xx, x0 is continuous at x=0, is

Note: Assume base of logarithm as e, everywhere.

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If fx is continuous at x=0, where fx=8x-2xkx-1,  x02,     x=0, then k is equal to
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If f is continuous at x=0, where fx=e3x-1sinx°x2, x0, then f0 is
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If fx=e5x-e2xsin 3x,x0k2,x=0 is continuous at x=0, then the value of k is

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In order that the function fx=x+1cotx is continuous at x=0, f0 must be defined as