Continuity and Differentiability questions
732 published questions with worked solutions.
- Let S = ( , ) R R : f(t) = (| |e^ |t| - ) (2|t|), t R , is a differentiable function . Then S is a subset of
- Let f(x) = cases (x - 1)^ 1 2 - x , & x > 1, x 2 k, & x = 2 cases The value of k for which f is continuous at x = 2 is -
- If the function f(x) = cases a| - x| + 1, & x 5 b|x - | + 3, & x > 5 cases is continuous at x = 5, then the value of a − b is:
- If f(x) = cases (p+1)x + x x , & x < 0 q, & x = 0 x + x^2 - x x^ 3/2 , & x > 0 cases is continuous at x = 0, then the ordered...
- Let f: R R be differentiable at c ∈ R and f(c) = 0. If g(x) = |f(x)|, then at x = c, g is:
- Let f be a differentiable function from R to R such that |f(x) - f(y)| 2|x - y|^ 3/2 , for all x, y ∈ R. If f(0) = 1 then _0^1...
- Let f: R R be a function defined as f(x) = cases 5, & if x 1 a + bx, & if 1 < x < 3 b + 5x, & if 3 x < 5 30, & if x 5 cases ....
- Let S be the set of all points in (−π, π) at which the function, f(x) = min sin x, cos x is not differentiable. Then S is a...
- Let K be the set of all real values of x where the function f(x) = sin|x| − |x| + 2(x − π) cos|x| is not differentiable. Then the...
- Let f(x) = cases -1, & -2 x < 0 x^2 - 1, & 0 x 2 cases and g(x) = |f(x)| + f(|x|). Then, in the interval (−2, 2), g is:
- Let f: (−1, 1) → R be a function defined by f(x) = -|x|, - 1 - x^2 . If K be the set of all points at which f is not...
- Let f: R R be a function such that f(x) = x^3 + x^2f'(1) + xf''(2) + f'''(3), x ∈ R. Then f(2) equals:
- Let f(x) = cases |x|, x^2 , & |x| 2 8 - 2|x|, & 2 < |x| 4 cases . Let S be the set of points in the interval (−4, 4) at which f...
- If the function f defined on (- 1 3 , 1 3 ) by f(x)= cases 1 x _e ( 1+3x 1-2x ), & when x 0 k, & when x=0 cases is continuous,...
- Let [t] denote the greatest integer t and _ x 0 x [ 4 x ]=A. Then the function, f(x)=[x^2] ( x) is discontinuous, when x is equal...
- If f(x)= cases (a+2)x+ x x & ; x<0 b & ; x=0 (x+3x^2)^ 1/3 -x^ 1/3 x^ 4/3 & ; x>0 cases is continuous at x = 0, then a + 2b is...
- Let f(x) = |2x² + 5|x| − 3|, x ∈ R. If m and n denote the number of points where f is not continuous and not differentiable...
- Let f : R → R be define as: f(x) = cases a - b 2x x^2 , & x < 0 x^2 + cx + 2, & 0 x 1 2x + 1, & x > 1 cases . If f is continuous...
- If the function f(x) = cases 72^x - 9^x - 8^x + 1 2 - 1 + x , & x 0 a _e2 _e3, & x = 0 cases is continuous at x = 0, then the...
- Let f : R → R be a function given by f(x) = cases 1 - 2x x^2 , & x < 0 , & x = 0 1 - x x , & x > 0 cases , where α, β ∈ R. If f...
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