having trouble with the Lagrange Problems. Please help on 5B and 6C. Thank you.

F(x) = enx , n= 4 1 = 4 = 4 5. Find a 4th degree Taylor polynomial for In x centered at x = 4. F ( A)= Flat (x- al Exalt ( x - a). Flu)= F( 4)= en (4) 2 : F" ( a ) + .. ( x ta)h F Y ( G ) F'(x ) : + 7 f a ) = 7 f" (a ) = - 1/16 76 " (a) = 1132 . Fullca A. Use the polynomial to approximate In (4.2). 2 8 F ( X ) 3 2 x = 4.2 - In 4 + 0.2 4 3 2 192 1024 = 1 435084 B. Find the Lagrange error bound on the interval [4, 4.5]. m = 24 1 Ry ( 45 / = 1024 Ru ( x ) = $:(4 ) (x-cut1 ( x ) : 24 K ( s ) X 5 6. Given f (x) = Vx A. Write a 2nd degree Taylor polynomial for f (x) about x = 4. ((x) = Kla) = F (4) = 2 *( X ) = 2 + ( x-4) . 4 + ( x-4)2 32 F'(x ) = 2 x-2 - Zx7 Fal= 4 P 2 ( X1 = 2 + 7 ( x - 4 ) - + F" CH) = x (- 2). x - 312-2 F" (al - - 32 - by ( x - 4 ) 2 4 x 3/2 B. Use the polynomial to approximate f (4.1). K( x ) = 2 + 4 ( . 1 ) - Gy ( 0. 1) 2 * = 4- 1 = 12. 024 F 4375 3 C. Find the Lagrange error bound for the approximation on the interval; [4, 4.1] m - 256 exact value = Jy. 1 = 2. 024 8 415 673 ( " ( * ) = 3 F X lexact - approx. 1 = 1. 92 31 365 x 10-6 666