Problem #7: Let f(x) = x, 0.3 x 1.7. Suppose that we approximate f(x) by the 2nd

Question

Problem #7: Let f(x) = x, 0.3 x 1.7. Suppose that we approximate f(x) by the 2nd degree Taylor polynomial T2(x) centered at a1. Taylor's inequaltiy gives an estimate for the error involved in this approximation Find the smallest possible value of the constant M referred to in Taylors Inequality. Enter your answer symbolically as in these examples Problem #7 Just save Submit Problem #7 for Grading Problem #7| Attempttl | Attempt#2 | Attempt #3 Your Answer: Your Mark Problem # 8: The curve y sy 36 x2 , -3 sxs4, is rotated about the x-axis. Find the area of the resulting surface . Enter your answer symbolically, as in these examples Problem #8 Suomit Problem #8 for Grading Attempt #1 Just Save | Attempte2 | Attempte3 Problem # Your Answer: Your Mark:

Explanation / Answer

Tf(x)=1/x2

f'(x)= -2/x3 f'(2)=-2/8=-1/4

f''(x)= -6/ x4  f''(2)=-6/16= -3/8

T(x) centred at a=1 gives

f(2)+f'(2)(x-2)+(f''(2)(x-2)2)/2

T(x)=1/4 -1/4(x-2) -3/16(x-2)2

T(1)=0.25-0.25*-1-0.1875*1=0.3125

f(1) =1

So |T(1)-f(1)|=0.6875=M

Similarly we can substitute different values of x in the taylor series as well as qctual function to get the absolute balue of M

for example taking x=0.5

T(0.5)=0.25-0.25*-1.5-0.875*2.25=-1.34375

f(0.5)=1/0.52=4

| T(0.5)-f)0.5)|=5.54375 not the smallest value of M

We have keep repeating it until we get the smallest vslue.

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