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Sia ? 6 years, 1 month ago
Let f(x) = 2x − {tex}|x|{/tex}
We have f(x)=2x - {tex}|x|{/tex}
{tex}\Rightarrow f(x)=\left\{\begin{array}{ll}{2 x-(-x)} & {\text { if } x<0} \\ {2 x-(x)} & {\text { if } x>0}\end{array}\right.{/tex}
Continuity at x=0
We have LHL as
{tex}\lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0^{-}} 2 x+x{/tex}
{tex}\Rightarrow{/tex} 0
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Sia ? 6 years, 1 month ago
You can use reverse rules to find antiderivatives. The easiest antiderivative rules are the ones that are the reverse of derivative rules you already know. These are automatic, one-step antiderivatives with the exception of the reverse power rule, which is only slightly harder.
You know that the derivative of sin <i>x</i> is cos <i>x</i>, so reversing that tells you that an antiderivative of cos <i>x</i> is sin <i>x</i>.
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Ravi Joshi 6 years, 1 month ago
1Thank You