X - 2-lim-x-33 - -x3-3 is where - is g-i-f is a3- Find a-

lim _ x→ 2 ^ + = lim _ h→ 0 f(2+h) =lim _ h→ 0 ( [2+h] ^ 3 3 [ 2+h 3 ] ^ 3 ) ⇒ ( 8 3 0) ⇒ 8 3 = a 3 a=8 ...

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Theorems for Continuity

x → 2+lim[x]3...

Question

$l i m x \to 2^{+} (\frac{[x]^{3}}{3} - {[\frac{x}{3}]}^{3})$ is (where [] is g.i.f) is $\frac{a}{3}$ . Find $a$ .

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lim x \to 2^{+} (\frac{| x |^{3}}{3} - {[\frac{x}{3}]}^{3}),

[x]

x

l_{1} = {lim}_{x \to 2^{+}} (x + [x]), l_{2} = {lim}_{x \to 2^{-}} (2 x - [x])

l_{3}

= {lim}_{x \to \frac{π}{2}} \frac{cos x}{x - \frac{π}{2}}

\lim_{x \to 3} f (x)

f (x) = \{\begin{cases} 4, & if x > 3 \\ x + 1, & if x < 3 \end{cases}

$l i m x \to 3 ([x - 3] + [3 - x] - x), where[.]denote the greatest integer function, is equal to:$

\lim_{x \to 3} f (x)

f (x) = \{\begin{cases} 4, & if x \geq 3 \\ x + 1, & if x < 3 \end{cases}

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