Home
Class 12
MATHS
Assuming x to be so small that x^2 and h...

Assuming `x` to be so small that `x^2` and higher power of `x` can be neglected, prove that

Text Solution

Verified by Experts

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`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Example|10 Videos
  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Concept Application Exercise 8.1|17 Videos
  • AREA

    CENGAGE PUBLICATION|Exercise Comprehension Type|2 Videos
  • CIRCLE

    CENGAGE PUBLICATION|Exercise For problems 3 and 4|2 Videos

Similar Questions

Explore conceptually related problems

If x is so small that x^3 and higher powers of x may be neglected, then ((1+x)^(3/2)-(1+1/(2x))^3)/((1-x)^(1/2)) may be approximated as A. 3x+3/8x^2 B. 1-3/8x^2 C. x/2-3/x^2 D. -3/8x^2

X-rays of wavelength lambda fall on photosensitive-surface emitting electrons. Assuming that the work function of the surface can be neglected, prove that the de-Bfoglie wave-length of eleectrons emitted will be root ((hlambda)/(2mc)) .What is threshold frequency?

If f(x)=x|x| , prove that f'(x)=2|x|

If f(x) = x|x| , prove that f'(1) = 2 .

If x in R ,a n da ,b ,c are in ascending or descending order of magnitude, show that (x-a)(x-c)//(x-b)(w h e r ex!=b) can assume any real value.

Prove that, 2 sin x+tan x ge3x ,where 0 le x le (pi)/(2) .

If f(x) is the probability distribution function of a random variable X and X can assume only two values x_1 and x_2 then the value of f(x_1)+f(x_2) is

If f(x)=x|x|,prove that f'(x)=2|x|.

Prove that if x is odd , then x^(2) is also odd.