Question

1)

Use linear approximation, i.e. the tangent line, to approximate 15.22 as follows: Let f(x) = z² and find the equation of the tangent line to f(x) at x = 15. Using this, find your approximation for 15.22

2)

3)

Answer 1

4 we have to use linear appronimation, ie. tangent line to approninate 15.2² follows Let flug = ne and find the equation of the tangent line to flu) at n = 15 we Know that eavation of tangent live to flnl is given f(x) = y = math where ma slope of tangent line at point ira 62 constant y-Intercept given f(4=r? x=a=15 f145) 3 = 225 we know slope is also given as ma f'( TX=15 so differentiate ful with respect ma f'(20) = 22 Now put u=15 for slope of targent line to play at 2511 m=free) Lucie 2015) = 30 So f(n)=y= 30xtb Now to find 6 ent HE IS and f(x) =92 225 225= 30x15th 225= 450th b = 22.5-450 b=-225

eauation of the the tangent line to Flu) at e=15 مد given as F(x) = 4= 30x~2250 f(x)= 3024-225 put 4= 15.2 in Now to equation appronimate 15.2² of tangent line f( 15.2) = (30X16.21-225 = 456-225 f(1522) = 231 the appronimation for 18.2² is 231