Question

simplify the following (2/3)^-2​

Answer 1

Answer:

$Find the Value of given Limit :-</p><p></p><p>\begin{gathered} \bigstar \: \: \: \: \rm\lim_{x \to 0} \: \bigg( \frac{sinx}{cosx} \bigg) \\ \end{gathered}★x→0lim(cosxsinx)</p><p></p><p>\large \dag† Answer :-</p><p></p><p>\begin{gathered}\red\dashrightarrow\underline{\underline{\sf  \green{The  \: Value \:  of  \: Given \:  Limit \:  is \:  0}} }\\ \end{gathered}⇢ The Value of Given Limit is 0</p><p></p><p>\large \dag† Pre - Required Knowledge :-</p><p></p><p>\begin{gathered} \displaystyle \large\bf \red\bigstar \: \: \orange{ \underbrace{ \underline{\blue{  \lim_{x \to 0} \small \bigg( \frac{f(x)}{g(x)} \bigg) = \dfrac{ \displaystyle \bf\lim_{x \to 0} f(x)}{ \displaystyle \bf\lim_{x \to 0} g(x)} }}}} \\ \end{gathered}★ x→0lim(g(x)f(x))=x→0limg(x)x→0limf(x)</p><p></p><p>Also,</p><p></p><p>\displaystyle \large\bf \red\bigstar \: \: \orange{ \underbrace{ \underline{\blue{  \lim_{x \to 0} \small \bigg( {f(x)}. \: {g(x)} \bigg) = { \displaystyle \bf\lim_{x \to 0} f(x)}{ \displaystyle . \: \bf\lim_{x \to 0} g(x)} }}}}★ x→0lim(f(x).g(x))=x→0limf(x).x→0limg(x)</p><p></p><p>And ,</p><p></p><p>\large\bf \red\bigstar \: \: \orange{ \underbrace{ \underline{  \blue{ \lim_{x \to 0} \small \bigg( \frac{sinx}{x} \bigg) }}}}★ x→0lim(xsinx)</p><p></p><p>And Also,</p><p></p><p>\large\bf \red\bigstar \: \: \orange{ \underbrace{ \underline{  \blue{ \lim_{x \to 0} \small \big( {cosx}\big) =cos0= 1 } }}}★ x→0lim(cosx)=cos0=1</p><p></p><p>\large \dag† Step by step Explanation :-</p><p></p><p>\begin{gathered} \large\: \: \: \: \rm\lim_{x \to 0} \: \bigg( \frac{sinx}{cosx} \bigg) \\ \end{gathered}x→0lim(cosxsinx)</p><p></p><p>\begin{gathered} \rm = \frac{ \displaystyle \rm\lim_{x \to 0} (sinx)}{ \displaystyle \rm\lim_{x \to 0} (cosx)} \\ \end{gathered}=x→0lim(cosx)x→0lim(sinx)</p><p></p><p>\begin{gathered} \large\rm = \frac{\displaystyle \rm\lim_{x \to 0} \: (sinx)}{\displaystyle \rm\lim_{x \to 0} \: (cosx)} \\ \end{gathered}=x→0lim(cosx)x→0lim(sinx)</p><p></p><p>⏩ Multiplying and Dividing Numerayor by x :-</p><p></p><p>\begin{gathered}\large = \frac{\displaystyle \rm\lim_{x \to 0} \: \bigg(\frac{xsinx}{x} \bigg) }{\displaystyle \rm\lim_{x \to 0} \: (cosx)} \\ \end{gathered}=x→0lim(cosx)x→0lim(xxsinx)</p><p></p><p>\begin{gathered} \large\rm = \frac{\displaystyle \rm\lim_{x \to 0}(x).\displaystyle \rm\lim_{x \to 0} \bigg( \frac{sinx}{x} \bigg)}{\displaystyle \rm\lim_{x \to 0}(cosx)} \\ \end{gathered}=x→0lim(cosx)x→0lim(x).x→0lim(xsinx)</p><p></p><p>\begin{gathered}\large = \frac{0.1}{1} \\ \end{gathered}=10.1</p><p></p><p>\underline{\Large \purple{ \underline { \pmb = \bf0}}}==0</p><p></p><p>$

Answer 2

Answer :

-2/3 × - 2/3

-2/3 × - 2/3 : - - = +

-2/3 × - 2/3 : - - = +4/9..

I'm weak in maths.. Is this your answer?