Math Editor

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​