AP EAMCET201922 Apr 2019Morning ShiftMathematicsLimitsActual
Define (f(x)= array cc 1+p x - 1-p x x , & if -1 x < 0 2 x+1 x-2 , & if 0 x 1 array . ) If ( _ x 0 f(x) ) exists, then (p= )
Options
- A-1
- B(- 1 2 )
- C( 1 2 )
- D1
Correct answer
B. (- 1 2 )
Step-by-step solution
Given, (f(x)= array cl 1+p x - 1-p x x , & if -1 x < 0 2 x+1 x-2 , & if 0 x 1 array . ) Now, RHL (= ) LHL (at (x=0 )) ( _ x 0⁺ 2 x+1 x-2 = _ x 0⁻ 1+p x - 1-p x x ) Apply L'Hospital rule in LHL ( - 1 2 = _ x 0⁻ p 2 1+p x + p 2 1-p x 1 ) ( - 1 2 = p 2 + p 2 - 1 2 =p p=- 1 2 )