Consider the following statements :
\( \mathbf{S}_{1}: \quad \lim _{x \rightarrow 0^{-}} \frac{[...
Consider the following statements :
\( \mathbf{S}_{1}: \quad \lim _{x \rightarrow 0^{-}} \frac{[x]}{x} \) is an indeterminate from (where [.] denotes greatest integer function ).
\( \mathbf{S}_{2}: \quad \lim _{x \rightarrow \infty} \frac{\sin \left(3^{x}\right)}{3^{x}}=0 \)
\( \mathbf{S}_{3}: \quad \lim _{x \rightarrow \infty} \sqrt{\frac{x-\sin x}{x+\cos ^{2} x}} \) does not exist.
\( \mathbf{S}_{4}: \quad \lim _{n \rightarrow \infty} \frac{(n+2) !+(n+1) !}{(n+3) !}(n \in N)=0 \)
State, in order, whether \( S_{1}, S_{2}, S_{3}, S_{4} \) are true or false
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