A function Tx is continuous and differentiable with values g

A function T(x) is continuous and differentiable with values given in the table below. Use the values in the table to estimate each of the following. Use best estimates and round your answers to two decimal places.

(c)

lim h0

The answer 1.88 , 1.89 , 17/9 and 15 is wrong

Solution

slope of secant line joining (25,17),(34,15) is (15-17)/(34-25) =-2/9

slope of secant line joining (34,15),(43,32) is (32-15)/(43-34) =17/9

lim _h0 ^{[T(34+h)-T(34)]}/_h represents slope of tangent line at x =34

slope of tangent line at x =34 can be estimated as the average of slopes of secant lines on either side of x =3

lim _h0 ^{[T(34+h)-T(34)]}/_h =[(-2/9)+(17/9)]/2

lim _h0 ^{[T(34+h)-T(34)]}/_h =(15/9)/2

lim _h0 ^{[T(34+h)-T(34)]}/_h =15/18

lim _h0 ^{[T(34+h)-T(34)]}/_h =0.83