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Find the value of 'a' for which the function f defined as <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-1"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-2">f</span><span class="MJXp-mo" id="MJXp-Span-3" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-4">x</span><span class="MJXp-mo" id="MJXp-Span-5" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-6" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mrow" id="MJXp-Span-7"><span class="MJXp-mo" id="MJXp-Span-8" style="margin-left: 0em; margin-right: 0em; vertical-align: -1.45em;"><span class="MJXp-right MJXp-scale2" style="font-size: 6.8em; margin-left: -0.394em;">{</span></span><span class="MJXp-mtable" id="MJXp-Span-9"><span><span class="MJXp-mtr" id="MJXp-Span-10" style="vertical-align: baseline;"><span class="MJXp-mtd" id="MJXp-Span-11" style="text-align: left;"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-12">a</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-13">s</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-14">i</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-15">n</span><span class="MJXp-mfrac" id="MJXp-Span-16" style="vertical-align: 0.25em;"><span class="MJXp-box MJXp-script"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-17">π</span></span><span class="MJXp-box" style="margin-top: -0.9em;"><span class="MJXp-denom"><span><span class="MJXp-rule" style="height: 1em; border-top: none; border-bottom: 1px solid; margin: 0.1em 0px;"></span></span><span><span class="MJXp-box MJXp-script"><span class="MJXp-mn" id="MJXp-Span-18">2</span></span></span></span></span></span><span class="MJXp-mo" id="MJXp-Span-19" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-20">x</span><span class="MJXp-mo" id="MJXp-Span-21" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mn" id="MJXp-Span-22">1</span><span class="MJXp-mo" id="MJXp-Span-23" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-24" style="margin-left: 0em; margin-right: 0.222em;">,</span></span><span class="MJXp-mtd" id="MJXp-Span-25" style="padding-left: 1em; text-align: left;"><span class="MJXp-mspace" id="MJXp-Span-26" style="width: 1em; height: 0em;"></span><span class="MJXp-mrow" id="MJXp-Span-27"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-28">x</span><span class="MJXp-mo" id="MJXp-Span-29" style="margin-left: 0.333em; margin-right: 0.333em;">≤</span><span class="MJXp-mn" id="MJXp-Span-30">0</span></span></span></span><span class="MJXp-mtr" id="MJXp-Span-31" style="vertical-align: baseline;"><span class="MJXp-mtd" id="MJXp-Span-32" style="padding-top: 0.4em; text-align: left;"><span class="MJXp-mstyle" id="MJXp-Span-33"><span class="MJXp-mfrac" id="MJXp-Span-34" style="vertical-align: 0.25em;"><span class="MJXp-box MJXp-script"><span class="MJXp-mi" id="MJXp-Span-35">tan</span><span class="MJXp-mspace" id="MJXp-Span-36" style="width: 0.222em; height: 0em;"></span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-37">x</span><span class="MJXp-mo" id="MJXp-Span-38">−</span><span class="MJXp-mi" id="MJXp-Span-39">sin</span><span class="MJXp-mo" id="MJXp-Span-40"></span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-41">x</span></span><span class="MJXp-box" style="margin-top: -0.9em;"><span class="MJXp-denom"><span><span class="MJXp-rule" style="height: 1em; border-top: none; border-bottom: 1px solid; margin: 0.1em 0px;"></span></span><span><span class="MJXp-box MJXp-script"><span class="MJXp-msubsup" id="MJXp-Span-42"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-43" style="margin-right: 0.05em;">x</span><span class="MJXp-mn MJXp-script" id="MJXp-Span-44" style="vertical-align: 0.5em;">3</span></span></span></span></span></span></span><span class="MJXp-mo" id="MJXp-Span-45" style="margin-left: 0em; margin-right: 0.222em;">,</span></span></span><span class="MJXp-mtd" id="MJXp-Span-46" style="padding-left: 1em; padding-top: 0.4em; text-align: left;"><span class="MJXp-mspace" id="MJXp-Span-47" style="width: 1em; height: 0em;"></span><span class="MJXp-mrow" id="MJXp-Span-48"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-49">x</span><span class="MJXp-mo" id="MJXp-Span-50" style="margin-left: 0.333em; margin-right: 0.333em;">></span><span class="MJXp-mn" id="MJXp-Span-51">0</span></span></span></span></span></span><span class="MJXp-mo" id="MJXp-Span-52" style="margin-left: 0em; margin-right: 0em;"></span></span></span></span><script type="math/tex" id="MathJax-Element-1"> f(x) = \left\{ \begin{array}{l l}asin\frac{\pi}{2}(x+1), & \quad { x \leq 0} \\ \large \frac{\tan\: x-\sin x}{x^3}, & \quad { x > 0} \end{array} \right. </script> is continuous at x = 0. - Clay6.com, a Free resource for your JEE, AIPMT and Board Exam preparation
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Find the value of 'a' for which the function f defined as f(x)={asinπ2(x+1),x0tanxsinxx3,x>0 is continuous at x = 0.

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