Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Most Important Selected Qs for JEE AdvancedMathematicsContinuity and Differentiability

STATEMENT 1: f(z)= Re (z) is a function where z complex number then f(z) is continuous but not differentiable STATEMENT 2: _ x 0 y 0 f(z+ z)-f(z) z = _ y 0 x 0 f(z+ z)-f(z) z for any point z

Options

  1. ABoth the statements are true and Statement 2 is correct explanation of Statement 1.
  2. BBoth the Statements are true and Statement 2 is not the correct explanation of Statement 1.
  3. CStatement 1 is true and Statement 2 is false.
  4. DStatement 1 is false and Statement 2 is true.

Correct answer

C. Statement 1 is true and Statement 2 is false.

Step-by-step solution

Continuity : for any point z, _ z z₀ f(z)= _ z z₀ x=x₀=f (z₀ ) . Non differentiable : for any point z , f^ (z)= _ z 0 f(z+ z)-f(z) z = _ z 0 x x+i y now _ x 0 y 0 x x+i y =0 and _ y 0 x 0 x x+i y =1

Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

Let R denote the set of all real numbers. Let f : R R be an arbitrary function and let g : R R be the function defined by g(x) = x f(x) , for all x R . Then which of the following 2026Consider the function f : (- 2 , 2 ) (- , ) defined by f(x) = (|x| + |x - 1|) x + [x x] , where [x x] is the greatest integer less than or equal to x x . Let be the total number of 2026For a real number , let [ ] denote the greatest integer less than or equal to . For a finite set S , let |S| denote the number of elements in the set S . Consider the functions f : 2026For the function f(x) = e^ |x| - |x| , x R , consider the following statements: Statement I: f is differentiable for all x R . Statement II: f is increasing in (- , - 2 ) . In the 2026Let f(x) = cases 1 3 , & x /2 b(1- x) ( -2x)^2 , & x > /2 cases . If f is continuous at x= /2 , then the value of ₀^ 3b-6 |x^2+2x-3| ,dx is: 2026Let f(x) = cases x^3 + 8 ; & x Then the number of points, where the function g f is discontinuous, is __________. 2026Let f(x)= cases e^ x-1 , & x<0 x^2-5x+6, & x 0 cases and g(x)=f(|x|)+|f(x)| . If the number of points where g is not continuous and is not differentiable are and respectively, then 2026The number of points, at which the function f(x) = 6x, 2 + 3x^2 + |x - 1| | |x^2 - 1 4 | | , x (- , ) , is not differentiable, is _____. 2026 Full Continuity and Differentiability list All Most Important Selected Qs for JEE Advanced PYQs