Q1) Q2) ?----------------------------------- Q3) Suppose g is a function which h
ID: 2838346 • Letter: Q
Question
Q1)
Q2)
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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
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