Question

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Solving time: 3 mins

# Let $f(x)=x_{2}+ax+3$. and $g(x)=x+b$, where $F(x)=lim_{n→∞}1+(x_{2})_{n}f(x)+(x_{2})_{n}g(x) $. If $F(x)$ is continuous at $x=1$ and $x=−1$ then find the value of $(a_{2}+b_{2})$.

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## Text solutionVerified

$F(x)=g(x)$ $x>1$

$=2f(x)+g(x) $ $x=1$

$=f(x)=2f(x)+g(x) −1<x<1x=−1 $

$=g(x)$ $x<−1$

If $F(x)$ is continuous at $x=1$

$F(1_{+})=F(1)=F(1_{−})$

$b=a+3$

If $F(x)$ is continuous at $x=−1$

$F(−1_{−})=F(−1)=F(−1_{+})$

$a+b=5$

$=2f(x)+g(x) $ $x=1$

$=f(x)=2f(x)+g(x) −1<x<1x=−1 $

$=g(x)$ $x<−1$

If $F(x)$ is continuous at $x=1$

$F(1_{+})=F(1)=F(1_{−})$

$b=a+3$

If $F(x)$ is continuous at $x=−1$

$F(−1_{−})=F(−1)=F(−1_{+})$

$a+b=5$

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**LIVE**classesQuestion Text | Let $f(x)=x_{2}+ax+3$. and $g(x)=x+b$, where $F(x)=lim_{n→∞}1+(x_{2})_{n}f(x)+(x_{2})_{n}g(x) $. If $F(x)$ is continuous at $x=1$ and $x=−1$ then find the value of $(a_{2}+b_{2})$. |

Updated On | May 2, 2023 |

Topic | Continuity and Differentiability |

Subject | Mathematics |

Class | Class 12 |

Answer Type | Text solution:1 Video solution: 1 |

Upvotes | 177 |

Avg. Video Duration | 9 min |