S. Find the first non-zero terms of the Taylor expansion for function x and a given value of a: then using obtained result evaluate this function, x, for a given values ot x. Crop one questbn at a tirne a. a=n/6, x=33 b. a-rt/4,x-4B C. a=Tt/3. X=63 d. a=rV2, Hint: Don't forget that angle x has to be substituted to expression of series in radians. Show your complete calculations. Compare your result with calculator value. Page Break 9. The time t (In years) for an investment to increase by i=O.10 (100/0) the interest rate is FO.06 (z 6%) is given by In(l i)Jr. For a numerical example given tEre it will be t: Inl.1/O.06 Evaluate this expression by using the first tour terms of the appropriate senes for follo"ng values ot i and r. You may use ready formulas from text for In (1+x) series. a. i=o.15. r=o.08 b. i-0.25, r:o.12 c. i-0.35, FO.15 d. i-045, r=o.19 Show your complete calculations. Compare your result calculator value. 10. Evaluate by using three terms of the expansion tor function sin x. Hint replace sin x with three terms of its series expanson. II. For the function given below sketch a graph Of the function, find indicated Fourier series coefficients (snow complete solutions) and calculate their numerical values. a. and a.