\(\lim_{x\to0}\dfrac{ln(1+(ln5)x)}{5^{x}}-1\)
\(1\)
\(ln 5\)
\(-1\)
\(5\)
\(\dfrac{1}{5}\)
The Correct Option is C
Solution and Explanation
\(\lim_{x\to0}\dfrac{ln(1+(ln5)x)}{5^{x}}-1\)
Substituting \(x=0\) , we get ,
\(=\)\(\dfrac{1+(ln5).0}{5^{0}}-1\)
\(=0-1\)
\(=-1\) (Ans)
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Concepts Used:
Limits
A function's limit is a number that a function reaches when its independent variable comes to a certain value. The value (say a) to which the function f(x) approaches casually as the independent variable x approaches casually a given value "A" denoted as f(x) = A.
If limx→a- f(x) is the expected value of f when x = a, given the values of ‘f’ near x to the left of ‘a’. This value is also called the left-hand limit of ‘f’ at a.
If limx→a+ f(x) is the expected value of f when x = a, given the values of ‘f’ near x to the right of ‘a’. This value is also called the right-hand limit of f(x) at a.
If the right-hand and left-hand limits concur, then it is referred to as a common value as the limit of f(x) at x = a and denote it by lim x→a f(x).