Continuity and Differentiability questions
732 published questions with worked solutions.
- If f(x)= x x+1 - x be a real-valued function then
- A function f(x) is defined in the interval [1,4) as follows: f(x)= cases _e[x], & 1 x<3 | _e x|, & 3 x<4. cases The graph of the...
- Let f(x) be a differentiable function and f(1)=2. If _ x 1 _2^ f(x) 2t x-1 ,dt=4 then the value of f'(1) is
- Let f(x) be a continuous function whose range is [2,6.5]. If h(x)= [ x+f(x) ], N, be continuous, where [ ] denotes the greatest...
- Let f(x)=[4+3 x], x (- 2, 2 ), where [x]= greatest integer less than or equal to x. The number of points of discontinuity of f(x)...
- One root of the equation 2 x + 1 = 2x lies in the interval
- Let f(x) = x^3 - 3x + t and f(0), f(1) are of opposite signs. Then the set of values of t is
- Let f(3) = 4 and f'(3) = 5. Then _ x 3 [f(x)], where [ ] denotes the greatest integer function, is
- If f(x) = cases 3x^2 + 12x - 1, & x [-1, 2] 37 - x, & x (2, 3] cases then
- Suppose f(x) is differentiable at x=1 and _ h 0 f(1+h) h =5. Then f'(1) equals
- If f is a real-valued differentiable function satisfying |f(x)-f(y)| (x-y)^2 for all x,y R and f(0)=0 then f(1) equals
- The function y= ||x|-1 | is differentiable for all x R except for the values
- In each question, match every entry of Column I with the correct entry of Column II. (An entry of Column II may be used more than...
- Let f(x) = x, 2 - x for all x R . Then
- If f(x) = [x - 1] + [x + 1] and g(x) = f f(x) then g'(3)
- Let the function f(x) be defined as follows f(x) = cases |x| & for -2 x 2 [x] & for 2 < x 4, cases where [ ] represents the...
- If f(x) is not differentiable finitely at x = 2 and f(x) + g(x) is differentiable finitely at x = 2 then
- The function f(x) = | x| (-2 x 2 ) is
- If f(x) = cases |x - 3| & for x 1 [4pt] x^2 4 - 3x 2 + 13 4 & for x < 1 cases then f(x) is
- If f(x) = cases x e^ -(1/|x| + 1/x) & for x 0 0 & for x = 0 cases then f(x) is
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