Q. 143.7( 3 Votes )

If , find all possible values of a.

Answer :

Given,


, we need to find value of n


So we will first find the limit and then equate it with 405 to get the value of n.


We need to find the limit for:


As limit can’t be find out simply by putting x = a because it is taking indeterminate form(0/0) form, so we need to have a different approach.


Let, Z =


Note: To solve the problems of limit similar to one in our question we use the formula mentioned below which can be derived using binomial theorem.


Formula to be used:


As Z matches exactly with the form as described above so we don’t need to do any manipulations–


Z =


Use the formula:


Z = 5(a)5–1 = 5a4


According to question Z = 405


5(a)4 = 405


a4 = 81 = 34 or (–3)4


Clearly on comparison we have –


a = 3 or –3


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