Library of functions Near zero: f (x) ~ f (0) + f' (0) x + f" (0) 2 . *=1+x+ -+0 (23) . sin (x) = x+0 (23) . cos (ac) = 1 -- 2 -+o (2 3 ) . In (1 + 2) = x - - +0 (23) . (1+ x) = 1+rx+ r (r - 1) 2 + O (x3 ) Powers 1 point possible (graded) What is the quadratic approximation to (1 + 3x) / near x = 0? (Do not enter the big-O term.)Approximation and compositions 2 points possible {graded} 3 Use a quadratic approximation for e\" to find an approximation to the function ex near it = 0. Find the magnitude of the error. (Do not enter the big-0 term.) 639% Error term is: O 0(32) 0 0(33) 0 0(3?) 0 0(39) Practice with products 1 1 point possible [graded] 1n(1a:) Consider near a: = 0. (1 + m)\" What is the quadratic approximation near a: = 0? (Do not enter the big-0 term.) In (1 m) (1 + m)2 N SmeiT You have used 0 of 5 attempts Save Practice with products 2 1 point possible [graded] sin (:13) Find the quadratic approximation of near x = 0 using the known approximations of 311106) and COS (a?) near cos2 (3:) a: = 0. (Do not enter the big-0 term.) Practice with products 3 \"I point possible [graded] Find the quadratic approximation for In (:13) sin (a: 1) near a: = 1. [Do not enter the big-O term.) Exponential 1 point possible (graded) What is the quadratic approximation of e * near * = 0? (Do not enter the big-O term.)Linear approximation of cubic 1 point possible [graded] What is the linear approximation for the function f (at) = :33 at a: = 0? [Do not enter the big-O term.) Smeit You have used 0 of 2 attempts Quadratic approximation of cubic \"I point possible [graded] What is the quadratic approximation for the function f (at) = :33 at a: = 0? (Do not enter the big-O term.)