1. [l6 Points] DETAILS MY NOTES Find the linear approximation, L(x), of f(x) = sin(x) at x = 1. 3 L(x) = Use the linear approximation to approximate sin( 57f ). (Round your answer to four decimal places.) L(5,Z)= 2. [-l6 Points] DETAILS MY NOTES Find the linear approximation, L(x), of f(x) = t/E at x = 4, L(x) = Use the linear approximation to approximate '/ 4.4. L(4.4) = 3. [-l6 Points] DETAILS MY NOTES Find the linear approximation, L(x), of f(x) = 3x x2 at x = 3. L(x) = Use the linear approximation to approximate f(3.3), L(3.3) = 4. [13 Points] DETAILS MY NOTES Use Newton's method to approximate J? to four consistent decimal places. 5. [-14 Points] DETAILS MY NOTES Use Newton's method to approximate the positive root of x3 + 7x 2 = 0 to three consistent decimal places. 6. [14 Points] DETAILS MY NOTES Use Newton's method to approximate the smallest positive root of sin(x) = e\" to three consistent decimal places. E 7. [14 Points] DETAILS MY NOTES Use Newton's method to approximate the root of |n(x) = 5 x to three consistent decimal places. E 8. [15 Points] DETAILS MY NOTES Use Newton's method to approximate all real roots of x4 x 3 = 0 to three consistent decimal places. (Enter your answers as a comma- separated list.)