4 Numerical method short questions

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2. A Maclaurin series for a function is given by ...... !5!3 )( 53  xx xxf What is the absolute relative approximate error if three terms are used for calculating ) f 2.1( ?

3. A Maclaurin series for a function is given by ...... !5!3 )( 53  xx xxf How many terms should be used in the series to consider that at least 2 significant digits are correct in your answer for ) f 1.0( ? 

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3. A hypothetical computer stores real numbers in floating point format in 10-bit words. The first bit is used for the sign of the number, the second bit for the sign of the exponent, the next three bits for the magnitude of the exponent, and the next five bits for the magnitude of the mantissa. Represent -0.0456 in the 10-bit format.

4. A hypothetical computer stores real numbers in floating point format in 10-bit words. The first bit is used for the sign of the number, the second bit for the sign of the exponent, the next three bits for the magnitude of the exponent, and the next five bits for the magnitude of the mantissa. What number does 1011010011 represent in the above given 10-bit format?