How do you use linear approximation about x=100 to estimate #1/sqrt(99.8)#? Calculus Applications of Derivatives Using Newton's Method to Approximate Solutions to Equations 1 Answer Anjali G Nov 9, 2016 #f(x) = 1/sqrtx# #f(x) = x^(-1/2)# #f(100) = 1/sqrt100 = 1/10 = .1# #f'(x) = (-1/2)(x^(-3/2))# #f'(100) = (-1/2)(100)^(-3/2) = -.0005# #L(x) = -.0005(x-100)+.1# #L(99.8) = -.0005(-.2)+.1 = .1001# Answer link Related questions How do you use Newton's Method to approximate #root5(20) # ? How do you use Newton's Method to approximate the value of cube root? How do you use Newton's Method to approximate the root of the equation #x^4-2x^3+5x^2-6=0# on... How do you use Newton's Method to approximate the positive root of the equation #sin(x)=x^2# ? If a rough approximation for ln(5) is 1.609 how do you use this approximation and differentials... How do you use linear approximation to estimate #g(2.95)# and #g(3.05)# if you know that #g(3)=-5#? How do you use a linear approximation to estimate #g(0.9)# and #g(1.1)# if we know that #g(1)=3#... How do you use differentials to estimate the value of #cos(63)#? When do you use newton's method? What is the local linearization of #e^sin(x)# near x=1? See all questions in Using Newton's Method to Approximate Solutions to Equations Impact of this question 4232 views around the world You can reuse this answer Creative Commons License