If , find all possible values of a.
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