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Q1) Q2) ?----------------------------------- Q3) Suppose g is a function which h

ID: 2838346 • Letter: Q

Question

Q1)

Q2)

?-----------------------------------

Q3)

Suppose g is a function which has continuous derivatives, and that g(8) = 3, g ?(8) = -2, g (8) = 1. (a) Find the Taylor polynomial of degree 2 for g near 8. Simplify all coefficients. P2(x)= (b) Use P2(x) to approximate g(7.9). Round your answer to two decimal places. Use the information in the table to calculate the limits below. Suppose P2(x) = a + bx + cx^2 is the second degree Taylor polynomial for the function f about x = 0. What can you say about the signs of a, b, c if f has the graph given below?

Explanation / Answer

f(0) = a   from graph it at x=0 graph is -ve

hence a < 0

take derivative : b + 2cx  

slope is +ve in graph , hence b + 2cx > 0

put x=0   :   b > 0

slope is also increasing

take derivative again

2c > 0   : c>0

Q2) L hospital rule :   f'(x)/h'(x) = f''(0)/h''(0)

: 7/8

f(x)/g(x) = f'(x)/g'(x) = 0/22 = 0

3)   a(x-8)^2 + b(x-8) + c

g(8) = c = 3

g'(8) = b = -2

g''(8) = 2a = 1

a = 1/2

1/2(x-8)^2 -2(x-8) + 3

1/2 [ -0.1 ]^2   -2[-0.1] + 3

1/200 + 0.2 + 3

3.205