Evaluate the following limit : lim(x→0)(e^x - x - 1)/2

Question

Evaluate the following limit : \(\lim\limits_{\text x \to0}\cfrac{e^{\text x}-\text x-1}2 \)

lim(x→0) (e^x - x - 1)/2

Answer 1

As we need to find  \(\lim\limits_{\text x \to0}\cfrac{e^{\text x}-\text x-1}2 \)

lim(x→0) (e^x - x - 1)/2

We can directly find the limiting value of a function by putting the value of the variable at which the limiting value is asked if it does not take any indeterminate form (0/0 or ∞/∞ or ∞-∞, .. etc.)

Let Z = \(\lim\limits_{\text x \to0}\cfrac{e^{\text x}-\text x-1}2 \)

 \(=0\)(not indeterminate)

As we got a finite value, so no need to do any modifications.

Hence,

\(\lim\limits_{\text x \to0}\cfrac{e^{\text x}-\text x-1}2 \) = 0