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Sandwich Theorem - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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68 Questions around this concept.
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For each $t \epsilon R$, let $[t]$ be the greatest integer less than or equal to $t$. Then
$
\lim _{x \rightarrow 0} x\left(\left[\frac{1}{x}\right]+\left[\frac{2}{x}\right]+\ldots .+\left[\frac{15}{x}\right]\right)
$
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Which of the following is true for the real valued functions
?
The integer for which
is a finite, non-zero real number, is
where [ ] denotes the greatest integer function:
.
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Concepts Covered - 1
Sandwich Theorem
Sandwich Theorem
Sandwich theorem is also known as the squeeze play theorem. It is typically used to find the limit of a function via comparison with two other functions whose limits are known or are easily calculated.
Sandwich Theorem
Let $f(x), g(x)$ and $h(x)$ be real functions such that $f(x) \leq g(x) \leq h(x)$ for all $x$ in the neighbourhood of $x=a$. If $\lim _{x \rightarrow a} f(x)=l=\lim _{x \rightarrow a} h(x)$, then $\lim _{x \rightarrow a} g(x)=l$.
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