Question
Download Solution PDFयदि फलन \(\rm f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {a + bx,\;\;}&{x < 1}\\ {5,}&{x = 1}\\ {b - ax,}&{x > 1} \end{array}} \right.\) स्थिरांक है, तो (a + b) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
फलन निरंतर होने के लिए:
LHL = RHL = f(x)
जहाँ LHL = \(\rm\mathop {\lim }\limits_{α \to 0}\)f(x - α) और RHL = \(\rm\mathop {\lim }\limits_{α \to 0}\)f(x + α)
गणना:
दिया गया है कि f(x) निरंतर फलन है
LHL = f(x) = RHL
\(\rm\mathop {\lim }\limits_{α \to 0}\) f(1 - α) = f(1)
\(\rm\mathop {\lim }\limits_{α \to 0}\) [a + b(1 - α)] = 5
\(\rm\mathop {\lim }\limits_{α \to 0}\) [a + b - bα] = 5
a + b = 5
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