f(x) = {((sin(a + 2)x + sinx)/x; x < 0), (b; x = 0), ((x + 3x2)1/3 - x

1.	f(x) = {((sin(a + 2)x + sinx)/x; x < 0), (b; x = 0), ((x + 3x2)1/3 - x1/3)/x4/3; x > 0) Function is continuous at x = 0, find a + 2b.
Answer» LHL = a + 3 f(0) = b RHL = lim_(h →0)((1 + 3h)^1/3 - 1)/h) = 1 ∴ a = - 2 b = 1 ∴ a + 2b = 0

f(x) = {((sin(a + 2)x + sinx)/x; x < 0), (b; x = 0), ((x + 3x2)1/3 - x1/3)/x4/3; x > 0) Function is continuous at x = 0, find a + 2b.

Answer»

LHL = a + 3

f(0) = b

RHL = lim_(h →0)((1 + 3h)^1/3 - 1)/h) = 1

∴ a = - 2

b = 1

∴ a + 2b = 0

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f(x) = {((sin(a + 2)x + sinx)/x; x &lt; 0), (b; x = 0), ((x + 3x2)1/3 - x1/3)/x4/3; x &gt; 0) Function is continuous at x = 0, find a + 2b.

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f(x) = {((sin(a + 2)x + sinx)/x; x < 0), (b; x = 0), ((x + 3x2)1/3 - x1/3)/x4/3; x > 0) Function is continuous at x = 0, find a + 2b.