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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits1 Mark
Question
Evaluate the following limits: $\lim _{y \rightarrow-3}\left[\frac{y^5+243}{y^3+27}\right]$
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Answer

$\lim _{y \rightarrow-3} \frac{y^5+243}{y^3+27}$
$=\lim _{y \rightarrow-3} \frac{\left(\frac{y^5+243}{y+3}\right)}{\left(\frac{y^3+27}{y+3}\right)} \quad \cdots\left[\begin{array}{l} \because y \rightarrow-3, y \neq-3, \\ \therefore y+3 \neq 0 \end{array}\right]$
$=\frac{\lim _{y \rightarrow-3}\left[\frac{y^5-(-3)^5}{y-(-3)}\right]}{\lim _{y \rightarrow-3}\left[\frac{y^3-(-3)^3}{y-(-3)}\right]} \quad \quad \ldots\left[\because \lim _{x \rightarrow 0} \frac{x^n- a ^n}{x- a \cdot}= n . a ^{n-1}\right]$
$=\frac{5(-3)^4}{3(-3)^2}$
$=\frac{5}{3} \times 9$
$=15$

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