 Hello and welcome to the session. In this session we will discuss the question which says that if x be so small that its squares and higher powers may be neglected, find the approximate value of 1 minus 3 by 2 h whole raise to power minus 3 plus 1 plus h whole raise to power 1 by 4 whole upon 1 minus h whole raise to power 1 by 3. Now before starting the solution of this question we should know about the result of approximation. Now we know that the expansion of 1 plus x raise to power m is equal to 1 plus nx plus n into n minus 1 over 1 into 2 into x square plus n into n minus 1 into n minus 2 over 1 into 2 into 3 into x cube plus so on up to infinity where absolute value of x is less than 1 and n be any fraction or a negative integer. Now as x is less than 1 so the terms of the above expansion go on decreasing and when x is very very small a stage may be reached when we may neglect the terms containing the higher powers of x. Thus if x be so small that its squares and higher powers may be neglected then the above expansion 1 plus x raise to power m will be equal to 1 plus nx so this is called the approximate value of 1 plus x raise to power m. Now this result will work out as a key idea for solving out this question and now we will start with the solution. Here we have to find the approximate value of 1 minus 3 by 2x whole raise to power minus 3 plus 1 plus x whole raise to power 1 by 4 whole upon 9 minus x raise to power 1 by 3. So expanding the above expressions this will be equal to 1 plus nx here n is minus 3 and x is minus 3 by 2x so it will be plus minus 3 into minus 3 by 2x plus so on plus 1 plus nx here n is 1 by 4 and x is x so it will be 1 by 4 into x plus so on whole upon 1 plus nx here n is 1 by 3 and x is minus x so it will be plus 1 by 3 into minus x plus so on. For finding out the approximate value of 1 plus x raise to power n it will be written as 1 plus nx as the term containing the higher powers of x are neglected. So here also neglecting the terms containing the higher powers of x this will be equal to 1 plus 9 by 2x plus 1 plus x by 4 whole upon 1 minus x by 3. Now opening the brackets this will be equal to 1 plus 1 plus 9 by 2x plus x by 4 whole upon 1 minus x by 3 further this is equal to 1 plus 1 is 2 plus taking the LCM it will be 4 here it will be 18x plus x whole upon 1 minus x by 3 this is equal to 2 plus 9 by 4x into taking this expression here so it will be 1 minus x by 3 whole raise to power minus 1 further this will be equal to 2 plus 19 by 4x into on expanding this it will be 1 plus nx as we are neglecting the higher powers of x so here 1 plus nx and here is minus 1 and x here is minus x by 3 so it will be minus 1 into minus x by 3 this will be equal to 2 plus 19 by 4x into 1 plus x by 3 now all multiplying these two expressions with each other this will be equal to 2 plus 2 by 3x plus 19 by 4x plus 19 by 12x2 now for finding out the approximate value we have to neglect the terms containing the higher powers of x so we will neglect this term so this will be equal to 2 plus on taking the LCM here it will be 12 and here it will be 3 into 4 is 12 and 4 into 2 is 8 so it will be 8x plus 4 into 3 is 12 and 3 into 19 is 57 so it will be 57x now this is equal to 2 plus 65 by 12x hence the approximate value 1 minus 3 by 2x whole raise to power minus 3 plus 1 plus x whole raise to power 1 by 4 whole upon 1 minus x whole raise to power 1 by 3 is equal to 2 plus 65 by 12x so this is the solution of the given question and that's all for the session hope you all have enjoyed the session