Math 5 Exercise 2

Exercise 2

L1(x)=(1.4−1.3)(1.4−1.1)(x−1.3)(x−1.1)

L2(x)=(1.3−1.4)(1.3−1.1)(x−1.4)(x−1.1)

L3(x)=(1.1−1.4)(1.1−1.3)(x−1.4)(x−1.3)

P2(x)=L1⋅y1+L2⋅y2+L3⋅y3=(1.4−1.3)(1.4−1.1)(x−1.3)(x−1.1)×3.14+(1.3−1.4)(1.3−1.1)(x−1.4)(x−1.1)×4.15+(1.1−1.4)(1.1−1.3)(x−1.4)(x−1.3)×5.65=1.50667+13.3x−8.66667x2

L1(x)=(−2−1)(−2−2)(−2−4)(x−1)(x−2)(x−4)

L2(x)=(1+2)(1−2)(1−4)(x+2)(x−2)(x−4)

L3(x)=(2+2)(2−1)(2−4)(x+2)(x−1)(x−4)

L4(x)=(4+2)(4−1)(4−2)(x+2)(x−1)(x−2)

P3(x)=L1⋅y1+L2⋅y2+L3⋅y3+L4⋅y4=(−2−1)(−2−2)(−2−4)(x−1)(x−2)(x−4)×25+(1+2)(1−2)(1−4)(x+2)(x−2)(x−4)×−8+(2+2)(2−1)(2−4)(x+2)(x−1)(x−4)×−15+(4+2)(4−1)(4−2)(x+2)(x−1)(x−2)×−23=1−10x+x2

L1(x)=(1−2)(1−3)(1−4)(1−5)(x−2)(x−3)(x−4)(x−5)

L2(x)=(2−1)(2−3)(2−4)(2−5)(x−1)(x−3)(x−4)(x−5)

L3(x)=(3−1)(3−2)(3−4)(3−5)(x−1)(x−2)(x−4)(x−5)

L4(x)=(4−1)(4−2)(4−3)(4−5)(x−1)(x−2)(x−3)(x−5)

L5(x)=(5−1)(5−2)(5−3)(5−4)(x−1)(x−2)(x−3)(x−4)

P4(x)=L1⋅y1+L2⋅y2+L3⋅y3+L4⋅y4+L5⋅y5=(1−2)(1−3)(1−4)(1−5)(x−2)(x−3)(x−4)(x−5)×0.10+(2−1)(2−3)(2−4)(2−5)(x−1)(x−3)(x−4)(x−5)×0.11+(3−1)(3−2)(3−4)(3−5)(x−1)(x−2)(x−4)(x−5)×0.13+(4−1)(4−2)(4−3)(4−5)(x−1)(x−2)(x−3)(x−5)×0.14+(5−1)(5−2)(5−3)(5−4)(x−1)(x−2)(x−3)(x−4)×0.16=0.16−0.125x+0.083333x2−0.02x3+0.00166667x4

P4(x)=L1⋅y1+L2⋅y2+L3⋅y3+L4⋅y4+L5⋅y5=(0.5−0.8)(0.5−1.5)(0.5−2.5)(0.5−4)(x−0.8)(x−1.5)(x−2.5)(x−4)×1.15+(0.8−0.5)(0.8−1.5)(0.8−2.5)(0.8−4)(x−0.5)(x−1.5)(x−2.5)(x−4)×1.77+(1.5−0.5)(1.5−0.8)(1.5−2.5)(1.5−4)(x−0.5)(x−0.8)(x−2.5)(x−4)×3.09+(2.5−0.5)(2.5−0.8)(2.5−1.5)(2.5−4)(x−0.5)(x−0.8)(x−1.5)(x−4)×4.67+(4−0.5)(4−0.8)(4−1.5)(4−2.5)(x−0.5)(x−0.8)(x−1.5)(x−2.5)×6.56=0.05065+2.27426x−0.1408x2−0.02312x3+0.004468x4

P4(x)=L1⋅y1+L2⋅y2+L3⋅y3+L4⋅y4+L5⋅y5=(1−2)(1−3)(1−4)(1−5)(x−2)(x−3)(x−4)(x−5)×0.25+(2−1)(2−3)(2−4)(2−5)(x−1)(x−3)(x−4)(x−5)×0.17+(3−1)(3−2)(3−4)(3−5)(x−1)(x−2)(x−4)(x−5)×0.11+(4−1)(4−2)(4−3)(4−5)(x−1)(x−2)(x−3)(x−5)×0.1+(5−1)(5−2)(5−3)(5−4)(x−1)(x−2)(x−3)(x−4)×0.08=0.23+0.1325x−0.15125x2+0.0425x3−0.00374997x4