Work the following on notebook paper. Use your calculator only on problem 8(b), 9(b), and 10(a). Show all work. 1 Find a fourth-degree Maclaurin polynomial for f(x) = e. 2. Find a sixth-degree Maclaurin polynomial for f(x) = cos x. 3. Find a fifth-degree Maclaurin polynomial for f(x)= x+1 4. Find a third-degree Taylor polynomial for f (x) = sin x, centered at x= 6 Find a fifth-degree Taylor polynomial for f(x) = centered at x = = 2. 1 1-x 6. Find a third-degree Taylor polynomial for f(x) = (x-4), centered at x = 4. 7. Find a fifth-degree Taylor polynomial for f(x) = In (x-1), centered at x = 2. 2x 8. (a) Find a Taylor polynomial of degree n = 4 for f(x) = e* centered at x = 3. (b) Find P (3.31). What is the value of (3.31) and the value of f (3.31)-P4 (3.31)|? 9. Let g be a function which has derivatives of all orders for all real numbers. Assume g(5)=3, g'(5)=-2, g" (5)=7, g"" (5)=-3. (a) Write the Taylor polynomial of degree 3 for g centered at x = 5. (b) Use the polynomial that you found in part (a) to approximate g (4.9).