Continuity and Differentiability questions
732 published questions with worked solutions.
- Let f(x) be a polynomial function of second degree. If f(1)=f(-1) and a,b,c are in AP, then f'(a),f'(b) and f'(c) are in
- Let f : [0, 3] R be defined by f(x) = min x–[x], 1+[x]–x where [x] is the greatest integer less than or equal to x. Let P denote...
- Let f:[0, ) [0,3] be a function defined by f(x)= cases t:0 t x , & 0 x 2+ x, & x> cases Then which of the following is true ?
- The function f(x)=|x^2-2x-3|.e^ |9x^2-12x+4| is not differentiable at exactly :
- If the function f(x)= cases 1 x _e ( 1+ x a 1- x b ), & x<0 , & x=0 ^2x- ^2x-1 x^2+1 -1 , & x>0 cases is continuous at x = 0,...
- A function f is defined on [–3, 3] as f(x)= cases |x|,2-x^2 , & -2 x 2 [|x|], & 2<|x| 3 cases where [x] denotes the greatest...
- The number of points, at which the function f(x)=|2x+1|-3|x+2|+|x^2+x-2|, x R is not differentiable, is ________.
- If f(x)= cases _0^x(5+|1-t|)dt, & x>2 5x+1, & x 2 cases , then
- Consider the function f(x) cases P(x) (x-2) , & x 2 7, & x=2 cases Where P(x) is a polynomial such that P"(x) is always a...
- Let f:R R be defined as f(x)= cases |x^2-5x+6| (5x-x^2-6) , & x<2 ^ ( x-2 x-[x] ) , & x>2 , & x=2 cases where [x] is the greatest...
- Let [t] denote the greatest integer less than or equal to t. Let f(x) = x – [x], g(x) = 1 – x + [x], and h(x) = min f(x), g(x) ,...
- Let a, b R, b 0, Define a function f(x)= cases a 2 (x-1), & for x 0 2x- 2x bx^3 , & for x>0 cases If f is continuous at x = 0,...
- Let f:R R be defined as f(x)= cases 2 (- x 2 ), & x<-1 |ax^2+x+b|, & -1 x 1 ( x), & x>1 cases If f(x) is continuous on R, then a...
- The number of points where the function f(x) = cases |2x^2 - 3x - 7|, & x -1 [4x^2 - 1], & -1 < x < 1 |x+1| + |x-2|, & x 1 cases...
- Let f(x) = cases (x - [x]) x - [x] , & x (-2, -1) 2x, 3[|x|] , & |x| < 1 1, & otherwise cases where [t] denotes greatest integer...
- Let f(x) = |4x^ 2 - 8x + 5| if 8x^ 2 - 6x + 1 0, and f(x) = [4x^ 2 - 8x + 5] if 8x^ 2 - 6x + 1 < 0, where [ ] denotes the...
- Let f(x) = [2x^ 2 + 1] and g(x) = 2x − 3 for x < 0 and 2x + 3 for x 0. Where [t] is the greatest integer t. Then, in the open...
- If the function f(x) = [log_e(1 − x + x^ 2 ) + log_e(1 + x + x^ 2 )]/( x − cos x), x (- /2, /2) − 0 , and f(0) = k, is continuous...
- If f(x) = x + a for x 0 and |x − 4| for x > 0, and g(x) = x + 1 for x < 0 and (x - 4)^ 2 + b for x 0, are continuous on R, then...
- Let f(x) = min 1, 1 + x sin x , 0 x 2 . If m is the number of points, where f is not differentiable and n is the number of...
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