79991 The function \(f: R \rightarrow R\) defined by
\(f(x)=\lim _{n \rightarrow \infty} \frac{\cos (2 \pi x)-x^{2 n} \sin (x-1)}{1+x^{2 n+1}-x^{2 n}}\)
continuous for all \(x\) in

79992 The values of \(a\) and \(b\) such that the function
defined by \(f(x)=\left\{\begin{array}{ll}7, \text { if } x \leq 2 \\ a x+b, \text { if } 2\lt x\lt 9 \\ 21, \text { if } x \geq 9\end{array}\right.\) is a
continuous fun

79993 Let \(f(x)\) be a function defined by
\(\mathbf{f}(\mathbf{x})=\left\{\begin{array}{cc}\mathbf{4 x}-\mathbf{5}, \text { if } & \mathbf{x} \leq \mathbf{2} \\ \mathbf{x}-\lambda, \text { if } & \mathbf{x}>2\end{array}\right.\) if \(\lim _{x \rightarrow 2} f(x)\) exists then the value of \(\lambda\) is

79994 If the function \(f(x)\), defined below is continues on the interval \([0,8]\), then
\(f(x)=\left\{\begin{array}{r}x^2+a x+b, 0 \leq x\lt 2 \\ 3 x+2,2 \leq x \leq 4 \\ 2 a x+5 b, 4\lt x \leq 8\end{array}\right\}\)

79995 If \(f(x)\), defined below is continuous at \(x=4\), then
\(f(x)=\left\{\begin{array}{l}\frac{x-4}{|x-4|}+a, & x\lt 4 \\ a+b, & \quad x=4 \\ \frac{x-4}{|x-4|}+b, & x>4\end{array}\right\}\)

79991 The function \(f: R \rightarrow R\) defined by
\(f(x)=\lim _{n \rightarrow \infty} \frac{\cos (2 \pi x)-x^{2 n} \sin (x-1)}{1+x^{2 n+1}-x^{2 n}}\)
continuous for all \(x\) in

79992 The values of \(a\) and \(b\) such that the function
defined by \(f(x)=\left\{\begin{array}{ll}7, \text { if } x \leq 2 \\ a x+b, \text { if } 2\lt x\lt 9 \\ 21, \text { if } x \geq 9\end{array}\right.\) is a
continuous fun

79993 Let \(f(x)\) be a function defined by
\(\mathbf{f}(\mathbf{x})=\left\{\begin{array}{cc}\mathbf{4 x}-\mathbf{5}, \text { if } & \mathbf{x} \leq \mathbf{2} \\ \mathbf{x}-\lambda, \text { if } & \mathbf{x}>2\end{array}\right.\) if \(\lim _{x \rightarrow 2} f(x)\) exists then the value of \(\lambda\) is

79994 If the function \(f(x)\), defined below is continues on the interval \([0,8]\), then
\(f(x)=\left\{\begin{array}{r}x^2+a x+b, 0 \leq x\lt 2 \\ 3 x+2,2 \leq x \leq 4 \\ 2 a x+5 b, 4\lt x \leq 8\end{array}\right\}\)

79995 If \(f(x)\), defined below is continuous at \(x=4\), then
\(f(x)=\left\{\begin{array}{l}\frac{x-4}{|x-4|}+a, & x\lt 4 \\ a+b, & \quad x=4 \\ \frac{x-4}{|x-4|}+b, & x>4\end{array}\right\}\)

79991 The function \(f: R \rightarrow R\) defined by
\(f(x)=\lim _{n \rightarrow \infty} \frac{\cos (2 \pi x)-x^{2 n} \sin (x-1)}{1+x^{2 n+1}-x^{2 n}}\)
continuous for all \(x\) in

79992 The values of \(a\) and \(b\) such that the function
defined by \(f(x)=\left\{\begin{array}{ll}7, \text { if } x \leq 2 \\ a x+b, \text { if } 2\lt x\lt 9 \\ 21, \text { if } x \geq 9\end{array}\right.\) is a
continuous fun

79993 Let \(f(x)\) be a function defined by
\(\mathbf{f}(\mathbf{x})=\left\{\begin{array}{cc}\mathbf{4 x}-\mathbf{5}, \text { if } & \mathbf{x} \leq \mathbf{2} \\ \mathbf{x}-\lambda, \text { if } & \mathbf{x}>2\end{array}\right.\) if \(\lim _{x \rightarrow 2} f(x)\) exists then the value of \(\lambda\) is

79994 If the function \(f(x)\), defined below is continues on the interval \([0,8]\), then
\(f(x)=\left\{\begin{array}{r}x^2+a x+b, 0 \leq x\lt 2 \\ 3 x+2,2 \leq x \leq 4 \\ 2 a x+5 b, 4\lt x \leq 8\end{array}\right\}\)

79995 If \(f(x)\), defined below is continuous at \(x=4\), then
\(f(x)=\left\{\begin{array}{l}\frac{x-4}{|x-4|}+a, & x\lt 4 \\ a+b, & \quad x=4 \\ \frac{x-4}{|x-4|}+b, & x>4\end{array}\right\}\)

79991 The function \(f: R \rightarrow R\) defined by
\(f(x)=\lim _{n \rightarrow \infty} \frac{\cos (2 \pi x)-x^{2 n} \sin (x-1)}{1+x^{2 n+1}-x^{2 n}}\)
continuous for all \(x\) in

79992 The values of \(a\) and \(b\) such that the function
defined by \(f(x)=\left\{\begin{array}{ll}7, \text { if } x \leq 2 \\ a x+b, \text { if } 2\lt x\lt 9 \\ 21, \text { if } x \geq 9\end{array}\right.\) is a
continuous fun

79993 Let \(f(x)\) be a function defined by
\(\mathbf{f}(\mathbf{x})=\left\{\begin{array}{cc}\mathbf{4 x}-\mathbf{5}, \text { if } & \mathbf{x} \leq \mathbf{2} \\ \mathbf{x}-\lambda, \text { if } & \mathbf{x}>2\end{array}\right.\) if \(\lim _{x \rightarrow 2} f(x)\) exists then the value of \(\lambda\) is

79994 If the function \(f(x)\), defined below is continues on the interval \([0,8]\), then
\(f(x)=\left\{\begin{array}{r}x^2+a x+b, 0 \leq x\lt 2 \\ 3 x+2,2 \leq x \leq 4 \\ 2 a x+5 b, 4\lt x \leq 8\end{array}\right\}\)

79995 If \(f(x)\), defined below is continuous at \(x=4\), then
\(f(x)=\left\{\begin{array}{l}\frac{x-4}{|x-4|}+a, & x\lt 4 \\ a+b, & \quad x=4 \\ \frac{x-4}{|x-4|}+b, & x>4\end{array}\right\}\)

79991 The function \(f: R \rightarrow R\) defined by
\(f(x)=\lim _{n \rightarrow \infty} \frac{\cos (2 \pi x)-x^{2 n} \sin (x-1)}{1+x^{2 n+1}-x^{2 n}}\)
continuous for all \(x\) in

79992 The values of \(a\) and \(b\) such that the function
defined by \(f(x)=\left\{\begin{array}{ll}7, \text { if } x \leq 2 \\ a x+b, \text { if } 2\lt x\lt 9 \\ 21, \text { if } x \geq 9\end{array}\right.\) is a
continuous fun

79993 Let \(f(x)\) be a function defined by
\(\mathbf{f}(\mathbf{x})=\left\{\begin{array}{cc}\mathbf{4 x}-\mathbf{5}, \text { if } & \mathbf{x} \leq \mathbf{2} \\ \mathbf{x}-\lambda, \text { if } & \mathbf{x}>2\end{array}\right.\) if \(\lim _{x \rightarrow 2} f(x)\) exists then the value of \(\lambda\) is

79994 If the function \(f(x)\), defined below is continues on the interval \([0,8]\), then
\(f(x)=\left\{\begin{array}{r}x^2+a x+b, 0 \leq x\lt 2 \\ 3 x+2,2 \leq x \leq 4 \\ 2 a x+5 b, 4\lt x \leq 8\end{array}\right\}\)

79995 If \(f(x)\), defined below is continuous at \(x=4\), then
\(f(x)=\left\{\begin{array}{l}\frac{x-4}{|x-4|}+a, & x\lt 4 \\ a+b, & \quad x=4 \\ \frac{x-4}{|x-4|}+b, & x>4\end{array}\right\}\)