If 
is finite, then (a + b) is equal to:
Text Solution
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To find the value of 
for which the following limit is finite:
we start by expanding the cosine functions using their Taylor series:
Substitute these expansions into the limit expression:
To ensure that the limit is finite, the linear and quadratic terms must sum to zero. Let's equate the constant terms first:
For the limit to be finite:
Equating the coefficients of 
:
Solving the second equation, we have:
Substitute 
back into the first equation to find 
:
Thus, the sum of 
and 
is:
Therefore, the correct value of 
is 
.
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