80004 If \(f(x)=f\left\{\begin{array}{l}\mathrm{ax}^{2}-b,-1\lt \mathrm{x}\lt 1 \\ \frac{1}{|\mathrm{x}|},|\mathrm{x}| \geq 1\end{array}\right.\) is differentiable at \(x=1\), then

80005 Let \(f: \mathrm{R} \rightarrow \mathrm{R}\) be the function defined by
\(f(x)=\left\{\begin{array}{cc}5, \text { if } x \leq 1 \\ a+b x, \text { if } 1\lt x\lt 3 \\ b+5 x, \text { if } 3 \leq x\lt 5 \\ 30, \text { if } x \leq 5\end{array}\right.\) then \(f\) is

80007 The function of \(f(x)=|x|+\frac{|x|}{x}\) is

80008 If \(f: R \rightarrow R\) defined by.
\(f(x)=\left\{\begin{array}{cc}\frac{1+3 x^{2}-\cos 2 x}{x^{2}} , \text { for } x \neq 0 \\ k , \text { for } x \neq 0\end{array}\right.\)
is continuous at \(x=0\), then \(k\) is equal to.

80009 If \([x]\) denotes the greatest integer not exceeding \(x\) and if the function \(f\) defined by
\(f(x)= \begin{cases}\frac{a+2 \cos x}{x^{2}}, (x\lt 0) \\ b \tan \frac{\pi}{(x+4)}, (x \geq 0)\end{cases}\)
is continuous at \(x=0\), then the ordered pair (a, b) is equal to

80004 If \(f(x)=f\left\{\begin{array}{l}\mathrm{ax}^{2}-b,-1\lt \mathrm{x}\lt 1 \\ \frac{1}{|\mathrm{x}|},|\mathrm{x}| \geq 1\end{array}\right.\) is differentiable at \(x=1\), then

80005 Let \(f: \mathrm{R} \rightarrow \mathrm{R}\) be the function defined by
\(f(x)=\left\{\begin{array}{cc}5, \text { if } x \leq 1 \\ a+b x, \text { if } 1\lt x\lt 3 \\ b+5 x, \text { if } 3 \leq x\lt 5 \\ 30, \text { if } x \leq 5\end{array}\right.\) then \(f\) is

80007 The function of \(f(x)=|x|+\frac{|x|}{x}\) is

80008 If \(f: R \rightarrow R\) defined by.
\(f(x)=\left\{\begin{array}{cc}\frac{1+3 x^{2}-\cos 2 x}{x^{2}} , \text { for } x \neq 0 \\ k , \text { for } x \neq 0\end{array}\right.\)
is continuous at \(x=0\), then \(k\) is equal to.

80009 If \([x]\) denotes the greatest integer not exceeding \(x\) and if the function \(f\) defined by
\(f(x)= \begin{cases}\frac{a+2 \cos x}{x^{2}}, (x\lt 0) \\ b \tan \frac{\pi}{(x+4)}, (x \geq 0)\end{cases}\)
is continuous at \(x=0\), then the ordered pair (a, b) is equal to

80004 If \(f(x)=f\left\{\begin{array}{l}\mathrm{ax}^{2}-b,-1\lt \mathrm{x}\lt 1 \\ \frac{1}{|\mathrm{x}|},|\mathrm{x}| \geq 1\end{array}\right.\) is differentiable at \(x=1\), then

80005 Let \(f: \mathrm{R} \rightarrow \mathrm{R}\) be the function defined by
\(f(x)=\left\{\begin{array}{cc}5, \text { if } x \leq 1 \\ a+b x, \text { if } 1\lt x\lt 3 \\ b+5 x, \text { if } 3 \leq x\lt 5 \\ 30, \text { if } x \leq 5\end{array}\right.\) then \(f\) is

80007 The function of \(f(x)=|x|+\frac{|x|}{x}\) is

80008 If \(f: R \rightarrow R\) defined by.
\(f(x)=\left\{\begin{array}{cc}\frac{1+3 x^{2}-\cos 2 x}{x^{2}} , \text { for } x \neq 0 \\ k , \text { for } x \neq 0\end{array}\right.\)
is continuous at \(x=0\), then \(k\) is equal to.

80009 If \([x]\) denotes the greatest integer not exceeding \(x\) and if the function \(f\) defined by
\(f(x)= \begin{cases}\frac{a+2 \cos x}{x^{2}}, (x\lt 0) \\ b \tan \frac{\pi}{(x+4)}, (x \geq 0)\end{cases}\)
is continuous at \(x=0\), then the ordered pair (a, b) is equal to

80004 If \(f(x)=f\left\{\begin{array}{l}\mathrm{ax}^{2}-b,-1\lt \mathrm{x}\lt 1 \\ \frac{1}{|\mathrm{x}|},|\mathrm{x}| \geq 1\end{array}\right.\) is differentiable at \(x=1\), then

80005 Let \(f: \mathrm{R} \rightarrow \mathrm{R}\) be the function defined by
\(f(x)=\left\{\begin{array}{cc}5, \text { if } x \leq 1 \\ a+b x, \text { if } 1\lt x\lt 3 \\ b+5 x, \text { if } 3 \leq x\lt 5 \\ 30, \text { if } x \leq 5\end{array}\right.\) then \(f\) is

80007 The function of \(f(x)=|x|+\frac{|x|}{x}\) is

80008 If \(f: R \rightarrow R\) defined by.
\(f(x)=\left\{\begin{array}{cc}\frac{1+3 x^{2}-\cos 2 x}{x^{2}} , \text { for } x \neq 0 \\ k , \text { for } x \neq 0\end{array}\right.\)
is continuous at \(x=0\), then \(k\) is equal to.

80009 If \([x]\) denotes the greatest integer not exceeding \(x\) and if the function \(f\) defined by
\(f(x)= \begin{cases}\frac{a+2 \cos x}{x^{2}}, (x\lt 0) \\ b \tan \frac{\pi}{(x+4)}, (x \geq 0)\end{cases}\)
is continuous at \(x=0\), then the ordered pair (a, b) is equal to

80004 If \(f(x)=f\left\{\begin{array}{l}\mathrm{ax}^{2}-b,-1\lt \mathrm{x}\lt 1 \\ \frac{1}{|\mathrm{x}|},|\mathrm{x}| \geq 1\end{array}\right.\) is differentiable at \(x=1\), then

80005 Let \(f: \mathrm{R} \rightarrow \mathrm{R}\) be the function defined by
\(f(x)=\left\{\begin{array}{cc}5, \text { if } x \leq 1 \\ a+b x, \text { if } 1\lt x\lt 3 \\ b+5 x, \text { if } 3 \leq x\lt 5 \\ 30, \text { if } x \leq 5\end{array}\right.\) then \(f\) is

80007 The function of \(f(x)=|x|+\frac{|x|}{x}\) is

80008 If \(f: R \rightarrow R\) defined by.
\(f(x)=\left\{\begin{array}{cc}\frac{1+3 x^{2}-\cos 2 x}{x^{2}} , \text { for } x \neq 0 \\ k , \text { for } x \neq 0\end{array}\right.\)
is continuous at \(x=0\), then \(k\) is equal to.

80009 If \([x]\) denotes the greatest integer not exceeding \(x\) and if the function \(f\) defined by
\(f(x)= \begin{cases}\frac{a+2 \cos x}{x^{2}}, (x\lt 0) \\ b \tan \frac{\pi}{(x+4)}, (x \geq 0)\end{cases}\)
is continuous at \(x=0\), then the ordered pair (a, b) is equal to