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Properties of Determinants

Let f(x)=e^x....

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Let f(x)=e^x.g(x), g(0)=4, g'(0)=2, then f'(0) equals

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f

g

be functions satisfying

f (x) = e^{x} g (x)

f (x + y) = f (x) + f (y), g (0) = 0

g^{'} (0) = 4, g

g^{'}

are continuous at

0

Q. Assertion :Let

f

g

be real-valued functions defined on interval

(- 1, 1)

g^{''} (x)

is countinuous,

g (0) \neq 0, g^{'} (0) = 0, g^{''} (0) \neq 0

f (x) = g (x) . sin x .

lim x \to 0 {g (x) \cdot cot x - g (0) \cdot c o sec x = f^{''} (0)},

f^{'} (0) = g (0) .

f (x) = e^{x} g (x), g (0) = 2, g^{'} (0) = 1

f^{'} (0)

Q. Assertion :Let f & g be real valued functions defined on interval (-1, 1) such that

g^{''} (x)

g (0) \neq 0

g^{'} (0) = 0

g^{n} (0) \neq 0

f (x) = g (x) sin x .

lim x \to 0 [g (x) cot x - g (0) c o s e c x] = f^{''} (0)

f^{'} (0) = g (0)

f (x) = e

^{x}

g (x),

g (0) = 1, g^{'} (0) = 3

f^{'} (0)

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