If f(x) = begincases (x2 + 3x - 10/x2 + 2x -15) , textwhen x x ≠ - 5 a , textwhen x = - 5 endcases is continuous at x = -5, then the value of âaâ will be

Question

If f(x) = begincases (x2 + 3x - 10/x2 + 2x -15) , textwhen x x ≠ - 5 a , textwhen x = - 5 endcases is continuous at x = -5, then the value of âaâ will be (A) 3/2 (B) 7/8 (C) 8/7 (D) 2/3

Tardigrade Admin · Accepted Answer

displaystyle lim x arrow-5 f(x)=((x-2)(x+5)/(x+5)(x-3)) =(-7/-8)=(7/8)

Q. If $f (x) = {\frac{x ^{2} + 3 x - 10}{x ^{2} + 2 x - 15}, a, when xx \neq = - 5 when x = - 5$ is continuous at $x = - 5$ , then the value of ‘ $a$ ’ will be

3/2

7/8

8/7

2/3

$x \to - 5 lim f (x) = \frac{( x - 2 ) ( x + 5 )}{( x + 5 ) ( x - 3 )}$
$= \frac{- 7}{- 8} = \frac{7}{8}$

Q. If f(x)={x2+2x−15x2+3x−10​,a,​whenxx=−5whenx=−5​ is continuous at x=−5, then the value of ‘a’ will be

3/2

7/8

8/7

2/3

x→−5lim​f(x)=(x+5)(x−3)(x−2)(x+5)​ =−8−7​=87​

Q. If $f (x) = {\frac{x ^{2} + 3 x - 10}{x ^{2} + 2 x - 15}, a, when xx \neq = - 5 when x = - 5$ is continuous at $x = - 5$ , then the value of ‘ $a$ ’ will be

$x \to - 5 lim f (x) = \frac{( x - 2 ) ( x + 5 )}{( x + 5 ) ( x - 3 )}$
$= \frac{- 7}{- 8} = \frac{7}{8}$