Continuity and Differentiability questions
732 published questions with worked solutions.
- Consider the following statements in respect of the given function : f(x)= cases x^3 |x| , & x 0 0, & x=0 cases I. f(x) is...
- If y= | ( 4 -x ) |, then what is dy dx at x= 4 equal to?
- Let f be a differentiable function such that f(x+y)=f(x)+f(y) for all x, y R. Which of the following statements is/are correct?...
- If f(x)=e^ |x| , then which one of the following is correct?
- If the function f(x)= cases a+bx, & x<1 5, & x=1 b-ax, & x>1 cases is continuous, then what is the value of (a+b)?
- Consider the following statements in respect of f(x)=|x|-1 : 1. f(x) is continuous at x=1. 2. f(x) is differentiable at x=0....
- Consider the following statements in respect of the function f(x)= ( 1 x^2 ), x 0 : 1. It is continuous at x=0, if f(0)=0. 2. It...
- Let the functions f: (-1, 1) R and g: (-1, 1) (-1, 1) be defined by f(x) = |2x - 1| + |2x + 1| and g(x) = x - [x], where [x]...
- Let f: (0, 1) R be the function defined as f(x) = [4x] (x - 1 4 )^2 (x - 1 2 ), where [x] denotes the greatest integer less than...
- If for p q 0, the function f(x) = (^ 7 p(729 + x) - 3)/(^ 3 729 + qx - 9) is continuous at x = 0, then
- Let a function f : R R be defined as f(x) = _ 0 ^ x (5 − |t − 3|)dt for x > 4 and f(x) = x^ 2 + bx for x 4. Where b R, If f is...
- Let f : R R be defined as f(x) = [e^ x ] for x < 0; ae^ x + [x - 1] for 0 x < 1; b + [ ( x)] for 1 x < 2; [e^ -x ] - c for x 2....
- Let the function f(x) = [log_e(1 + 5x) − log_e(1 + x)]/x for x 0 and f(x) = 10 for x = 0 be continuous at x = 0. The is equal to
- If [t] denotes the greatest integer t, then number of points, at which the function f(x) = 4|2x + 3| + 9[x + 1/2] − 12[x + 20] is...
- The number of points, where the function f : R R, f(x) = |x − 1| cos|x − 2| sin|x − 1| + (x - 3)|x^ 2 - 5x + 4|, is NOT...
- The value of k which makes f(x)= cases x & x 0 k & x=0 cases continuous at x=0, is
- Let a Z and [t] be the greatest integer . Then the number of points, where the function f(x) = [a + 13sinx], x (0, ) is not...
- Let k and m be positive real numbers such that the function f(x) = cases 3x^2+k x+1 , & 0<x<1 ^2+k^2, & x 1 cases is...
- Let f : (–2, 2) R be defined by f(x)= cases x[x], & -2<x<0 (x-1)[x], & 0 x<2 cases Where [x] denotes the greatest integer...
- Let f(x) = [x^2-x]+|-x+[x]|, where x and [t] denotes the greatest integer less than or equal to t. Then, f is :
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