Find the approximations T_10, M_10, and S_10 for integral^2_0 e^5x dx and the corresponding errors E_T, E_M, and E_S. Round your answers to five decimal places. T_10 = E_T = M_10 = E_M = S_10 = E_S = 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^2 x/dx^2(e^5x)| lessthanorequalto K on (0, 2)? Do not round your answer. K = Use this value of K to determine the least n such that T_n is guaranteed to be accurate to within 0.000 l (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^4 x/dx^4 (e^5x) 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):
Show transcribed image text Find the approximations T_10, M_10, and S_10 for integral^2_0 e^5x dx and the corresponding errors E_T, E_M, and E_S. Round your answers to five decimal places. T_10 = E_T = M_10 = E_M = S_10 = E_S = 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^2 x/dx^2(e^5x)| lessthanorequalto K on (0, 2)? Do not round your answer. K = Use this value of K to determine the least n such that T_n is guaranteed to be accurate to within 0.000 l (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^4 x/dx^4 (e^5x) 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):