5 The Algorithm for Newton's Method LEARNING OBJECTIVE: Approximate the solutions of equations by using derivatives (Newton's method). Write Newton's formula used to approximate a solution of the equation - '2: + '1 - 4 11:0 and find the third iteration value. Be sure to verify both parts of the answer are correct when making your selection. " :. 3.435491 SCI-I 2 - The Linear Approximation Error I f(x) - L(x) I LEARNING OBJECTIVE: Find the error in calculations using linear approximation. KOOOD Consider the function f(x) = e* near x = 0. Find the linear approximation error when using the linear approximation to estimate e 0.45 ( a.) -1.45 ( b.) 1.45 ( C.) -0.1183 O d.) 0.11834 Approximation of Measurement Error Using Differentials LEARNING OBJECTIVE: Approximate the error in calculations using differentials. A sphere is to be designed with a radius of2.25 feet. Use differentials to estimate the maximum error when measuring the surface area of the sphere if the possible error in measuring the radius is 0.15 feet. (Hint: The formula for the surface area of a Sphere is .3: . 2411.2.) SUBMIT MY ANSWER 3 - The Differential of f LEARNING OBJECTIVE: Calculate the differential of a function using derivatives. KOOOD Let f(x) = (7x2 +1). Find the differential, of. O a.) of = 14xsec(7x2 + 1)tan(7x2+1) b.) of = 14xsec(x)tan(x)dx O c.) df = 14xsec(7x2 + 1)tan(7x2 +1)dx d.) of = 14xsec(x)tan(x) SUBMIT MY ANSWER1 Linear Approximation LEARNING OBJECTIVE: Approximate the values of functions by using tangent lines. Find the linear approximation of s'" - '=