MCQ
Choose the correct answer.
$\lim\limits_{\text{x} \rightarrow 0}\frac{|\sin\text{x}|}{\text{x}}$ is equal to:
$\lim\limits_{\text{x} \rightarrow 0}\frac{|\sin\text{x}|}{\text{x}}$ is equal to:
- A1
- B-1
- CDoes not exist
- DNone of these.
Solution:
Given $\lim\limits_{\text{x} \rightarrow 0}\frac{|\sin\text{x}|}{\text{x}}$
$\text{L}.\text{H}.\text{L}=\lim\limits_{\text{x} \rightarrow 0}\frac{-\sin\text{x}}{\text{x}}=-1$
$\text{R}.\text{H}.\text{L}=\lim\limits_{\text{x} \rightarrow 0}\frac{\sin\text{x}}{\text{x}}=1$
$\text{L}.\text{H}.\text{L}\neq\text{R}.\text{H}.\text{L}$
So, the limit does not exist.
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$0$
In the expansion of $\Big(\frac{1}{2}\text{x}^{\frac{1}{3}}+\text{x}^{\frac{-1}{5}}\Big)^{8},$ the term independent of x is:
$\text{T}_{5}$
$\text{T}_{6}$
$\text{T}_{7}$
$\text{T}_{8}$
What is the length of foot of perpendicular drawn from the point P(3, 4, 5) on y-axis.
$\sqrt{41}$
$\sqrt{34}$
$5$
$\text{None of these.}$