Find the value of a such that the function ( f(x)=left{begin{array}{cc}frac{2 x^{2}-2}{x-1} & x neq 1 3 a-1 & x=1end{array}right. ) is continuous at ( x=1 ) ?

Question

Find the value of a such that the function ( f(x)=left{begin{array}{cc}frac{2 x^{2}-2}{x-1} & x neq 1  3 a-1 & x=1end{array}right. ) is continuous at ( x=1 ) ?

Accepted Answer

Step:1 ：( lim_{x to 1} frac{2x^2 - 2}{x - 1} = 3a - 1 )Step:2 ：( lim_{x to 1} frac{2(x^2 - 1)}{x - 1} = 3a - 1 )Step:3 ：( lim_{x to 1} frac{2(x - 1)(x + 1)}{x - 1} = 3a - 1 )Step:4 ：( lim_{x to 1} 2(x + 1) = 3a - 1 )Step:5 ：( 2(1 + 1) = 3a - 1 )Step:6 ：( 4 = 3a - 1 )Step:7 ：( a = frac{5}{3} )

Answer

Step: 1 ：( lim_{x to 1} frac{2x^2 - 2}{x - 1} = 3a - 1 )Step: 2 ：( lim_{x to 1} frac{2(x^2 - 1)}{x - 1} = 3a - 1 )Step: 3 ：( lim_{x to 1} frac{2(x - 1)(x + 1)}{x - 1} = 3a - 1 )Step: 4 ：( lim_{x to 1} 2(x + 1) = 3a - 1 )Step: 5 ：( 2(1 + 1) = 3a - 1 )Step: 6 ：( 4 = 3a - 1 )Step: 7 ：( a = frac{5}{3} )

Find the value of a such that the function \( f(x)=\left\{\begin{array}{cc}\frac{2 x^{2}-2}{x-1} & x \neq 1 \\ 3 a-1 & x=1\end{array}\right. \) is continuous at \( x=1 \) ?

Answer

Popular Problems