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Assuming `x`to be so small that `x^2`and higher power of `x`can be neglected, prove that |
Answer» We have, `((1+3/4x)^(-4)(16-3x)^(1//2))/((8+x)^(2//3))=((1+3/4x)^(-4)(16)^(1//2)(1-(3x)/(16))^(1//2))/(8^(2//3)(1+x/8)^(2//3))` `= (1+3/4x)^(-4) (1-(3x)/(16))^(1//2) (1+(x)/(8))^(-2//3)` `{1+(-4) (3/4x)}{1+1/2 ((-3x)/(16))}{1+(-2/3)(x/8)}` `= (1-3x)(1-3/32x)(1-x/12)` `= (1-3x-3/(32)x)(1-x/12)` [neglecting `x^(2)`] `= (1-99/32x)(1-x/12)=1-(99)/(32)x-(x)/(12)` [neglecting `x^(2)`] `1 - (305)/(96) x` |
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