$\displaystyle \lim_{x \to 1}$$\left\{log_{e}\left(e^{x\left(x-1\right)}-e^{x\left(1-x\right)}\right)-log_{e}\left(4x\left(x-1\right)\right)\right\}$ is equal to :
- $-2\,log_e\,2$
- $1$
- $1-\,log_e\,2$
- $-\,log_e\,2$
The Correct Option is D
Solution and Explanation
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Concepts Used:
Continuity & Differentiability
Definition of Differentiability
f(x) is said to be differentiable at the point x = a, if the derivative f ‘(a) be at every point in its domain. It is given by
Definition of Continuity
Mathematically, a function is said to be continuous at a point x = a, if
It is implicit that if the left-hand limit (L.H.L), right-hand limit (R.H.L), and the value of the function at x=a exist and these parameters are equal to each other, then the function f is said to be continuous at x=a.
If the function is unspecified or does not exist, then we say that the function is discontinuous.