1.

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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