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Fractional Part Function

Write the con...

Question

Write the converse of a conditional statement.

"If Left hand limit = Right hand limit, then we say that limit exists".

(i.e. ${lim}_{x \to a} f (x) = f (a)$ )

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Solution

"If limit exists, then LHL = RHL"

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Similar questions

If the right and left hand limits coincide, we call that common value as the limit of f(x) at x = a and denote it by

For the limit $lim x \to a f (x)$ to exist, f(a) should be defined

lim x \to a f (x)

=

lim x \to a^{-} f (x) = l a n d lim x \to a^{+} f (x) = m

l \neq m .

= {\begin{matrix} 2 x^{2} & x is rational 1 - x, & x is irrational \end{matrix}

f

{lim}_{x \to a} f (x)

=

{lim}_{x \to a^{-}} f (x) = l a n d {lim}_{x \to a^{+}} f (x) = m

l \neq m .

⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} 2 | x |, & x \leq - 1 2 x, & - 1 \leq x \leq 0 x + 1, & 0 < x \leq 1 2 & x > 1 \end{matrix}

f (x)

lim x \to a f (x)

=

{lim}_{x \to a^{-}} f (x) = l a n d {lim}_{x \to a^{+}} f (x) = m

l \neq m .

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} x^{2} + | x |, & x < - 5 25 & x = - 5 \frac{3 x^{2}}{5} + 15 & x > - 5 \end{matrix}

x = - 5

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