Find the approximations T_10. M_10. and S_10 for integral^2_0 e^3x dx and the co

Question

Find the approximations T_10. M_10. and S_10 for integral^2_0 e^3x dx and the corresponding errors E_T, E_M, and E_S. Round your answers to five decimal places. Now let's use the Error Bounds given in your textbook (or your notes) to see how large we would need to make n to ensure T_n M_n, and S_n are accurate to within 0.0001. First of all. what is the least value K such that |d^2x/dx^2(e^3x)| lessthanorequalto K on (0, 2)? Do not round your answer Use this value of K to determine the least n such that T_n is guaranteed to be accurate to within 0.0001 (you should round up to the next whole number). Use this value of K to determine the least n such that M_n is guaranteed to be accurate to within 0.0001 (you should round up to the next whole number): What is the least value L such that |d^2x/dx^2(e^3x)| lessthanorequalto L on (0, 2)? Do not round your answer. L = Use this value of L to determine the least n such that S_n is guaranteed to be accurate to within 0.0001 (you should round up to the next even whole number):

Explanation / Answer

T10 = 138.14328

M10 = 132.15172

S10 = 134.23553

ET = 12.10286

EM = 24.20573

ES = 0.58094

K = 9e6

For trapezoidal rule n = 4920

For Mid point rule n = 3479

L = 81e6

For simpson rule n = 88

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