If the function  f(x)=\left\{\begin{matrix} a\left | \pi-x \right | +1,&x\leq 5 \\ b\left | x-\pi \right |+3,& x> 5 \end{matrix}\right.   is continuous x=5  at , then the value of   a-b   is :

  • Option 1)

    \frac{2}{\pi+5}

  • Option 2)

    \frac{-2}{\pi+5}

  • Option 3)

    \frac{2}{\pi-5}

  • Option 4)

    \frac{2}{5-\pi}

 

Answers (1)

f(x)=\left\{\begin{matrix} a\left | \pi-x \right | +1,&x\leq 5 \\ b\left | x-\pi \right |+3,& x> 5 \end{matrix}\right.

 

\lim_{x\rightarrow 5^{-}}f(x)=\lim_{x\rightarrow 5^{+}}f(x)

 

\\=a\left | \pi-5 \right |+1=b \left |5- \pi \right |+3\\\\\\\:a\left | \pi-5 \right |=b \left |5- \pi \right |+2

\\a(5-\pi)-b(5-\pi)=2\\\\\:(5-\pi)(a-b)=2

(a-b)=\frac{2}{5-\pi}

 


Option 1)

\frac{2}{\pi+5}

Option 2)

\frac{-2}{\pi+5}

Option 3)

\frac{2}{\pi-5}

Option 4)

\frac{2}{5-\pi}

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