How do you use a linear approximation or differentials to estimate #tan44º#? Calculus Applications of Derivatives Using Newton's Method to Approximate Solutions to Equations 1 Answer Ananda Dasgupta Jul 25, 2016 #~~ 0.965# Explanation: The derivative of #tan theta# is #sec^2 theta#, so that to a first order in #delta theta# we have #tan(theta - delta theta) = tan(theta) -sec^2 theta xx delta theta# To estimate #tan 44^circ# we must use #theta = pi/4# and #delta theta = pi/180# (remember that in calculus angles must be measured in radians) so that #tan 44^circ ~~ tan (pi/4)-sec^2 (pi/4) xx pi/180 = 1-2 xx pi/180 ~~ 0.965# 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 12282 views around the world You can reuse this answer Creative Commons License