Answer
$\dfrac{3}{4}$
Work Step by Step
In order to simplify the above expression, we will use the following rules.
$(a) \lim\limits_{x \to a} [p(x) \cdot q(x)]=\lim\limits_{x \to a} p(x) \lim\limits_{x \to a} q(x) \\ (b) \lim\limits_{x \to a} k(x)=k(a)$
where $a$ as a constant.
Thus, we have:
$\lim\limits_{x\to 0}\dfrac{3 \sin x+\cos x-1}{4x}\\=\lim\limits_{x\to 0}\dfrac{3 \sin x}{4x} +\lim\limits_{x\to 0} \dfrac{\cos x-1}{4x} \\=\dfrac{3}{4} [\lim\limits_{x\to 0}[(\dfrac{\sin{x}}{x}))+\dfrac{1}{4} [\lim\limits_{x\to 0} \dfrac{\cos x-1}{x}]\\=\dfrac{3}{4}+\dfrac{1}{4} \times (0) \\=\dfrac{3}{4}$
