Continuity and Differentiability questions
732 published questions with worked solutions.
- If f(x) = (27 - 2x)^ 1 3 - 3 9 - 3(243 + 5x)^ 1 5 , x 0 is continuous at x = 0, then the value of f(0) is
- If f(x) is continuous at point x=0 where f(x)= cases 3 x+5 x a^x-1 , & x<0 [2mm] 2 2 , & x=0 [2mm] 8x+2x x b^x-1 , & x>0 cases...
- If the function f(x)= ( 5x-8 8-3x )^ 3 2x-4 , for x 2 is continuous at x = 2 then the value of f(2) is...
- If the function f(x)= 2 2 -( x+ x)^3 1- 2x is continuous at x= 4 , then the value of f ( 4 ) is…
- f(x)= cases [x^2]-[-x^2], & x 3 k, & x=3 cases is continuous at x = 3, then k = where [ ] is greatest integer function
- If f(x) = cases mx + 1, & x 2 x + n, & x > 2 cases is continuous at x = 2 , (m, n Z) then
- If the function f(x) defined by f(x) = cases ax+1 & if x 3 bx+3 & if x > 3 cases is continuous at x = 3, then (a - b) = …..
- Let [x] denotes the greatest integer less than or equal to x and f(x) = [ ^2x], then which of the following is true?
- If f(x)= cases 8^x-4^x-2^x+1^x x^2 , & if x>0 [2mm] e^x x+ix+ 4, & if x<0, i R cases is continuous at x = 0, then the value of...
- If f(x) = cases 8^x - 4^x - 2^x + 1 x^2 , & x > 0 [2mm] e^x x + x + 4, & x 0 cases is continuous at x = 0 then the value of 1000...
- If f(x)= cases 1- 4x x^2 & if x<0 & if x=0 x (16+ x)^ 12 -4 & if x>0 cases is continuous at x = 0 Then a =
- If the function f(x)= cases x+a 2 x & if 0 x 4 2x x+b & if 4 <x 2 a 2x-b x & if 2 <x cases is continuous in [0, ] then a-b=
- If f(x)= 10^x+7^x-14^x-5^x 1- x , x 0 is continuous at x=0, then the value of f(0) is
- Let f: R R is differentiable function having f(3) = 3, f'(3) = 1 27 and g(x) = cases _ 3 ^ f(x) 3t^2 x - 3 ,dt & , if x 3 K & ,...
- If f(x)= ( ^2x) 3x^2 , x 0 is continuous at x = 0 then f(0) =
- Let f(x)= cases x^4-5x^2+4 |(x-1)(x-2)| , & x 1,2 [2mm] 6, & x=1 [1mm] 12, & x=2 cases then f(x) is continuous on the set
- If the function f(x)= cases ax- bx cx- bx , & if x 0 -1, & if x=0 cases is continuous at x = 0, then a^2,b^2,c^2 are in
- If f(x)= cases 9^x-2 3^x+1 (1+3x) 2x , & if x 0 a( b)^c, & if x=0 cases is continuous at x=0, then a+b+c=
- If x + |y| = 2y, then y as a function of x, at x = 0 is
- Statement 1: A function f : R → R is continuous at x_0 if and only if _ x x_0 f(x) exists and _ x x_0 f(x) = f(x_0) Statement 2:...
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