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Temperature. Repeat Problem 61 for
61. Temperature. The temperature (in degrees Celsius) in an artificial habitat is made to change according to the equation
Use a Taylor series at 0 to approximate the average temperature over the time interval [0, 2] to within ±0.005.
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- 1. Find the first 4 terms of the Taylor series for the following functions: 1 (a) In x centered at a=1, (b) – centered at a=1. 2. Find the first 3 terms of the Taylor series for the function sin Tx centered at a=0.5. Use your answer to find an approximate value to sin(+-) 2 10arrow_forward(1) (a) Show that, for any positive integer n, n² + 3n =an(n − 1) - › (²1) ² ¹ (¹1)-¹ 2n for some a, ß> 0. Give the values of a and 3. Hint: solve the above equation for a and 3, your answers should be positive numbers. (b) Find the sum the series n²+3n 2n n=0 Hint: consider using derivatives of the geometric series and part (a). + ßnarrow_forward2x 1. Find a power series representation for f(x) = 1 + x² 2. Use your answer in III.1 to find a power series representation for g(x) = ln(1 + x²).arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage