<div class="question xl:text-lg px-4 py-2.5"><p>Let <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D6FC TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D6FC TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D6FC TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container>, <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D6FD TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D6FD TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D6FD TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi></math></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container> <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mo class="mjx-n"><mjx-c class="mjx-c2208"></mjx-c></mjx-mo></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mo class="mjx-n"><mjx-c class="mjx-c2208"></mjx-c></mjx-mo></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mo class="mjx-n"><mjx-c class="mjx-c2208"></mjx-c></mjx-mo></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∈</mo></math></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container> R be such that <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-munder><mjx-row><mjx-base style="padding-left: 0.038em;"><mjx-texatom texclass="OP"><mjx-mo class="mjx-n"><mjx-c class="mjx-c6C"></mjx-c><mjx-c class="mjx-c69"></mjx-c><mjx-c class="mjx-c6D"></mjx-c></mjx-mo></mjx-texatom></mjx-base></mjx-row><mjx-row><mjx-under style="padding-top: 0.167em;"><mjx-texatom size="s" texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D465 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c2192"></mjx-c></mjx-mo><mjx-mn class="mjx-n"><mjx-c class="mjx-c30"></mjx-c></mjx-mn></mjx-texatom></mjx-under></mjx-row></mjx-munder><mjx-mo class="mjx-n"><mjx-c class="mjx-c2061"></mjx-c></mjx-mo><mjx-texatom space="2" texclass="ORD"><mjx-mfrac><mjx-frac><mjx-num><mjx-nstrut></mjx-nstrut><mjx-texatom size="s" texclass="ORD"><mjx-texatom texclass="ORD"><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D465 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup></mjx-texatom><mjx-mi class="mjx-n" space="2"><mjx-c class="mjx-c73"></mjx-c><mjx-c class="mjx-c69"></mjx-c><mjx-c class="mjx-c6E"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c2061"></mjx-c></mjx-mo><mjx-mo class="mjx-n"><mjx-c class="mjx-c28"></mjx-c></mjx-mo><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D6FD TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D465 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c29"></mjx-c></mjx-mo></mjx-texatom></mjx-num><mjx-dbox><mjx-dtable><mjx-line></mjx-line><mjx-row><mjx-den><mjx-dstrut></mjx-dstrut><mjx-texatom size="s" texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D6FC TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D465 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c2212"></mjx-c></mjx-mo><mjx-mi class="mjx-n"><mjx-c class="mjx-c73"></mjx-c><mjx-c class="mjx-c69"></mjx-c><mjx-c class="mjx-c6E"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c2061"></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="2"><mjx-c class="mjx-c1D465 TEX-I"></mjx-c></mjx-mi></mjx-texatom></mjx-den></mjx-row></mjx-dtable></mjx-dbox></mjx-frac></mjx-mfrac></mjx-texatom><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-munder><mjx-row><mjx-base style="padding-left: 0.038em;"><mjx-texatom texclass="OP"><mjx-mo class="mjx-n"><mjx-c class="mjx-c6C"></mjx-c><mjx-c class="mjx-c69"></mjx-c><mjx-c class="mjx-c6D"></mjx-c></mjx-mo></mjx-texatom></mjx-base></mjx-row><mjx-row><mjx-under style="padding-top: 0.167em;"><mjx-texatom size="s" texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D465 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c2192"></mjx-c></mjx-mo><mjx-mn class="mjx-n"><mjx-c class="mjx-c30"></mjx-c></mjx-mn></mjx-texatom></mjx-under></mjx-row></mjx-munder><mjx-mo class="mjx-n"><mjx-c class="mjx-c2061"></mjx-c></mjx-mo><mjx-texatom space="2" texclass="ORD"><mjx-mfrac><mjx-frac><mjx-num><mjx-nstrut></mjx-nstrut><mjx-texatom size="s" texclass="ORD"><mjx-texatom texclass="ORD"><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D465 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup></mjx-texatom><mjx-mi class="mjx-n" space="2"><mjx-c class="mjx-c73"></mjx-c><mjx-c class="mjx-c69"></mjx-c><mjx-c class="mjx-c6E"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c2061"></mjx-c></mjx-mo><mjx-mo class="mjx-n"><mjx-c class="mjx-c28"></mjx-c></mjx-mo><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D6FD TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D465 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c29"></mjx-c></mjx-mo></mjx-texatom></mjx-num><mjx-dbox><mjx-dtable><mjx-line></mjx-line><mjx-row><mjx-den><mjx-dstrut></mjx-dstrut><mjx-texatom size="s" texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D6FC TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D465 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c2212"></mjx-c></mjx-mo><mjx-mi class="mjx-n"><mjx-c class="mjx-c73"></mjx-c><mjx-c class="mjx-c69"></mjx-c><mjx-c class="mjx-c6E"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c2061"></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="2"><mjx-c class="mjx-c1D465 TEX-I"></mjx-c></mjx-mi></mjx-texatom></mjx-den></mjx-row></mjx-dtable></mjx-dbox></mjx-frac></mjx-mfrac></mjx-texatom><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-munder><mjx-row><mjx-base style="padding-left: 0.038em;"><mjx-texatom texclass="OP"><mjx-mo class="mjx-n"><mjx-c class="mjx-c6C"></mjx-c><mjx-c class="mjx-c69"></mjx-c><mjx-c class="mjx-c6D"></mjx-c></mjx-mo></mjx-texatom></mjx-base></mjx-row><mjx-row><mjx-under style="padding-top: 0.167em;"><mjx-texatom size="s" texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D465 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c2192"></mjx-c></mjx-mo><mjx-mn class="mjx-n"><mjx-c class="mjx-c30"></mjx-c></mjx-mn></mjx-texatom></mjx-under></mjx-row></mjx-munder><mjx-mo class="mjx-n"><mjx-c class="mjx-c2061"></mjx-c></mjx-mo><mjx-texatom space="2" texclass="ORD"><mjx-mfrac><mjx-frac><mjx-num><mjx-nstrut></mjx-nstrut><mjx-texatom size="s" texclass="ORD"><mjx-texatom texclass="ORD"><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D465 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup></mjx-texatom><mjx-mi class="mjx-n" space="2"><mjx-c class="mjx-c73"></mjx-c><mjx-c class="mjx-c69"></mjx-c><mjx-c class="mjx-c6E"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c2061"></mjx-c></mjx-mo><mjx-mo class="mjx-n"><mjx-c class="mjx-c28"></mjx-c></mjx-mo><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D6FD TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D465 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c29"></mjx-c></mjx-mo></mjx-texatom></mjx-num><mjx-dbox><mjx-dtable><mjx-line></mjx-line><mjx-row><mjx-den><mjx-dstrut></mjx-dstrut><mjx-texatom size="s" texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D6FC TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D465 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c2212"></mjx-c></mjx-mo><mjx-mi class="mjx-n"><mjx-c class="mjx-c73"></mjx-c><mjx-c class="mjx-c69"></mjx-c><mjx-c class="mjx-c6E"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c2061"></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="2"><mjx-c class="mjx-c1D465 TEX-I"></mjx-c></mjx-mi></mjx-texatom></mjx-den></mjx-row></mjx-dtable></mjx-dbox></mjx-frac></mjx-mfrac></mjx-texatom><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mrow data-mjx-texclass="OP"><mo data-mjx-texclass="OP">lim</mo></mrow><mrow data-mjx-texclass="ORD"><mi>x</mi><mo accent="false" stretchy="false">→</mo><mn>0</mn></mrow></munder><mo data-mjx-texclass="NONE">⁡</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>x</mi><mn>2</mn></msup></mrow><mi>sin</mi><mo data-mjx-texclass="NONE">⁡</mo><mo stretchy="false">(</mo><mi>β</mi><mi>x</mi><mo stretchy="false">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>α</mi><mi>x</mi><mo>−</mo><mi>sin</mi><mo data-mjx-texclass="NONE">⁡</mo><mi>x</mi></mrow></mfrac></mrow><mo>=</mo><mn>1</mn></math></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container>. Then 6(<mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D6FC TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D6FC TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D6FC TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container> + <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D6FD TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D6FD TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D6FD TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi></math></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container>) equals _________.</p></div>