Q75.If f(x) = { 5x + 1, xx >≤22 (1) f(x) is not continuous at x = 2 (2) f(x) is everywhere differentiable (3) f(x) is continuous but not differentiable at x = 2 (4) f(x) is not differentiable at x = 1
What This Question Tests
This question evaluates continuity and differentiability of a piecewise function where one part is defined by an integral with an absolute value, requiring analysis at critical points.
Concepts Tested
Formulas Used
Left Hand Limit = Right Hand Limit = f(a) for continuity
Left Hand Derivative = Right Hand Derivative for differentiability
Fundamental Theorem of Calculus
📚 NCERT Sections This Tests
1.3 — Define The Following Terms:
Chemistry Class 11 · Chapter 1
1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.
14.2 — Which Of The Statements Given In Exercise 14.1 Is True For P-Type
Physics Class 12 · Chapter 14
14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
1.1 — Define The Term Solution. How Many Types Of Solutions Are Formed? Write Briefly
Chemistry Class 11 · Chapter 1
1.1 Define the term solution. How many types of solutions are formed? Write briefly about each type with an example.
📋 Question Details
- Chapter
- Differentiation
- Topic
- Continuity and Differentiability of Piecewise Functions
- Year
- 2021
- Shift
- 25 Jul Shift 2
- Q Number
- Q75
- Type
- Multi concept
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
More from this Chapter
Q79.Let f(x) = x|x| and g(x) = sin x. Statement-1 : gof is differentiable at x = 0 and its derivative is continuous at that point. Statement-2 : gof is twice differentiable at x = 0 . (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-2 is not a correct explanation for Statement-1 Statement-1 (3) Statement-1 is true, Statement-2 is false (4) Statement-1 is false, Statement-2 is true
Q80.Let y be an implicit function of x defined by x2x −2xx cot y −1 = 0 . Then y′(1) equals (1) −1 (2) 1 (3) log 2 (4) −log 2
Q79.Let f : (−1, 1) →R be a differentiable function with f(0) = −1 and f ′(0) = 1 . Let g(x) = [f(2f(x) + 2)]2 . Then g′(0) = (1) −4 (2) 0 (3) −2 (4) 4
Q78. d2x equals dy2 (1) d2y −1 dy −3 (2) d2y dy −2 −( dx2 ) ( dx ) ( dx2 )( dx ) (3) −( dx2d2y )( dxdy ) −3 (4) ( dx2d2y ) −1