1. Find the first four terms of the Taylor series for the following functions: (a) In x centered at a = 1 (b) centred at a = 1 (c) sin x centered at a = 2. Find the first 3 terms of the Taylor series for the function sin x centered at a = 0.5. Use your answer to find an approximate value to sin (+: 1 (+). 10/ 3. Find the Taylor Series Expansion for x + x 2 centered at a = 1. 4. Find the first 4 terms in the Taylor series for (x-1) ex near x = 1. 5. Find the first three terms of the Maclaurin Series for the following (a) sin (x) (b) (c) 1-x2 x 6. (a) Evaluate the integral for sin x dx by finding the Maclaurin approximation to the integrand with 3 terms. (b) Evaluate the integral exactly and compare. 7. Find the Maclaurin Series for xsin x 8. Find the Maclaurin Series for sin x using the series for cos 2x 9. Find the Maclaurin Series for the function e* and sin x, and hence expand esinx up to the term x4. Hence integrate esinx dx. 10. Write down the Maclaurin Series for the function f(x) = sinx and hence for sinx f(x) = Use this series to find an appropriate value of the integral fo keeping the first three terms in the Maclaurin series. sinx dx by