Continuity and Differentiability questions
732 published questions with worked solutions.
- Let f and g be real valued functions defined on interval (-1,1) such that g''(x) is continuous, g(0) 0, g'(0) = 0, g''(0) 0, and...
- Let [ ] denote the greatest integer function, and let f(x) = 2 x, x^2 . Let S = x (-2,2): the function g(x)=|x|[x^2] is...
- Let f(x) = cases ax^2+2ax+3 4x^2+4x-3 , & x - 3 2 , 1 2 b, & x=- 3 2 , 1 2 cases be continuous at x=- 3 2 . If fof(x)= 7 5 , then...
- If f(x) = cases a|x| + x^2 - 2 |x|( |x|) x & , x 0 b & , x = 0 cases is continuous at x = 0, then a + b is equal to :
- If the function f(x) = e^x(e^ x - x -1) + _e( x + x) - x x - x is Continuous at x=0, then the value of f(0) is equal to
- Let , R be such that the function f(x) = cases 2 (x^2-2)+2 x, & x<1 ( +3)x+( - ), & x 1 cases be differentiable at all x R . Then...
- Consider the following three statements for the function f: (0, ) R defined by f(x) = | _e x|-|x-1|: (I) f is differentiable for...
- If the function f(x) = cases 2 x (k_1+1)x + (k_2-1)x , & x < 0 4, & x=0 2 x _e ( 2+k_1x 2+k_2x ), & x>0 cases is continuous at x...
- Let [x] denote the greatest integer function, and let m and n respectively be the numbers of points, where the function f(x) =...
- Let f(x) = cases 5, & x > 2 1+x+[x], x+2[x] , & 0 x 2 3x, & x < 0 cases where [.] denotes greatest integer function. If and are...
- Let f(x) = cases (1+ax)^ 1/x , & x<0 1+b, & x=0 (x+4)^ 1/2 -2 (x+c)^ 1/3 -2 , & x>0 cases be continuous at x = 0. Then e^abc is...
- Let m and n be the number of points at which the function f(x) = x, x^3, x^5, …x^ 21 , x R , is not differentiable and not...
- If the function f(x) = ( x) - ( x) x - x is continuous at x = 0, then f(0) is equal to ______.
- Let f:R R be a continuous onto function satisfying f(x)+f(-x)=0, x R. If f(-3)=2 and f(5)=4, then the minimum number of roots of...
- One root of the equation - + 12=0 lies in the interval
- Let S = t R : f(x) = |x - | (e^ |x| - 1) |x| is not differentiable at t . Then the set S is equal to :
- If the function f defined as f(x) = 1 x - k - 1 e^ 2x - 1 , x 0, is continuous at x = 0, then the ordered pair (k, f(0)) is equal...
- Let f: [-1, 3] R be defined as f(x) = cases |x| + [x], & -1 x < 1 x + |x|, & 1 x < 2 x + [x], & 2 x 3 cases where [t] denotes the...
- Let f(x) = 15 − |x − 10|; x ∈ R. Then the set of all values of x, at which the function, g(x) = f(f(x)) is not differentiable, is:
- If the function f defined on ( 6 , 3 ) by f(x) = cases 2 x - 1 x - 1 , & x 4 k, & x = 4 cases is continuous, then k is equal to:
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