Let `f(x) = x|x|` and `g(x) = sin x` Statement-1: gof is differentiable at x=0 and derivative is continous at that point. Statement-2: gof is twice differentiable at x=0
A
Statement 1 is ture, statement 2 is true, statement 2 is a correct explanation for statement 1.
B
Statement 1 is ture, statement 2 is true, statement 2 is not a correct explanation for statement 1.
C
Statement 1 is ture, statement 2 is false.
D
Statement 1 is false, statement 2 is true.
Text Solution
AI Generated Solution
Topper's Solved these Questions
LIMITS, CONTINUITY AND DIFFERENTIABILITY
ML KHANNA|Exercise MISCELLANEOUS EXERCISE (MATCHING ENTRIES) |9 Videos
INVERSE CIRCULAR FUNCTIONS
ML KHANNA|Exercise Self Assessment Test|25 Videos
LINEAR PROGRAMMING
ML KHANNA|Exercise Self Assessment Test|8 Videos
Similar Questions
Explore conceptually related problems
Let f(x)=x|x| and g(x)=s in x Statement 1 : gof is differentiable at x=0 and its derivative is continuous at that point Statement 2: gof is twice differentiable at x=0 (1) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for statement 1 (2) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for statement 1. (3) Statement 1 is true, statement 2 is false. (4) Statement 1 is false, Statement 2 is true
Let f(x)=x^2+x+1 and g(x)=sinx . Show that fog!=gof .
Statement-1: If f and g are differentiable at x=c, then min (f,g) is differentiable at x=c. Statement-2: min (f,g) is differentiable at x=c if f(c ) ne g(c )
Let f(x)={x^n sin (1/x) , x!=0; 0, x=0; and n>0 Statement-1: f(x) is continuous at x=0 and AA n>0. and Statement-2: f(x) is differentiable at x=0 AA n>0 (1) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (2) Statement-1 is True, Statement-2 is True Statement-2 is NOT a correct explanation for Statement-1. (3) Statement-1 is True, Statement-2 is False (4) Statement-1 is False, Statement-2 is True.
Let f(x) = x|x| . The set of points, where f (x) is twice differentiable, is ….. .
Let f(x)=|x| and g(x)=|x^(3)|, then f(x) and g(x) both are continuous at x=0 (b) f(x) and g(x) both are differentiable at x=0 (c) f(x) is differentiable but g(x) is not differentiable at x=0 (d) f(x) and g(x) both are not differentiable at x=0
Let f(x)=|x-1|+|x-2| and g(x)={min{f(t):0<=t<=x,0<=x<=3 and x-2,x then g(x) is not differentiable at
Prove that f(x)={x sin((1)/(x)),x!=0,0,x=0 is not differentiable at x=0
Statement I f(x) = |cos x| is not derivable at x = (pi)/(2) . Statement II If g(x) is differentiable at x = a and g(a) = 0, then |g|(x)| is non-derivable at x = a.
ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -MISCELLANEOUS EXERCISE (ASSERTION/ REASONS)
