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If x is so small that x2 and higher powers of x can be neglected, then (1−x)1/5(9+2x)1/2(3+4x) is approximately equal to:
Explanation
Concept:
Expansion of (1+x)n when |x| < 1:
Calculation:
Let E=(1−x)1/5(9+2x)1/2(3+4x)
⇒E=(9+2x)1/2(3+4x)(1−x)−1/5
⇒E=[91/2(1+92x)1/2][3(1+34x)](1−x)−1/5
⇒E=[3(1+92x)1/2][3(1+34x)](1−x)−1/5
Expanding and neglecting higher powers of x:
⇒E=9(1+92×21x)(1+34x)(1−(−51)x)
⇒E=9(1+91x)(1+34x)(1+51x)
Neglecting the higher powers during multiplication:
⇒E=9(1+91x+34x)(1+51x)
Explanation
Concept:
Expansion of (1+x)n when |x| < 1:
Calculation:
Let E=(1−x)1/5(9+2x)1/2(3+4x)
⇒E=(9+2x)1/2(3+4x)(1−x)−1/5
⇒E=[91/2(1+92x)1/2][3(1+34x)](1−x)−1/5
⇒E=[3(1+92x)1/2][3(1+34x)](1−x)−1/5
Expanding and neglecting higher powers of x:
⇒E=9(1+92×21x)(1+34x)(1−(−51)x)
⇒E=9(1+91x)(1+34x)(1+51x)
Neglecting the higher powers during multiplication:
⇒E=9(1+91x+34x)(1+51x)
