Question

Let y = (x) be defined parametrically as y = t2 + t |t|x = 2t – |t|t Ïµ R Then at x = 0, find (x) and discuss continuity.

Solution

Correct option is

As,              y = t2 + t |t|

and             x = 2t – |t|  

Thus, when t ≥ 0                               

⟹ x = 2t – t = ty = t2 + t2 = 2t2.

∴           x =   and    y = 2t2

⟹        y = 2x2 ∀ x ≥ 0.  

Again when,

          t < 0

⟹     x = 2t + t = 3t        and    y = t2 – t2 = 0.

⟹     y = 0 for all x < 0. 

Hence, (x) =  which is clearly  

Continuous for all as shown graphically.

SIMILAR QUESTIONS

Q1

 for what value of kf (x) is continuous at x = 0?

Q2

      

Determine a and b such that f (x) is continuous at x = 0.

Q3

Find the points of discontinuity of 

Q4

 

   

Determine the form of g(x) = f ( f (x)) and hence find the point of discontinuity if g, if any.

Q5

The left hand derivative of f (x) = [x] sin (πx) at x = kk is an integer, is:

Q6

Which of the following functions is differentiable at x = 0?

Q7

Let f (x) = [n + p sin x], x Ïµ (0, π), n Ïµ Z and p is a prime number, where [.] denotes the greatest integer function. Then find the number of points where f (x) is not Differential.

Q8

, then draw the graph of f (x) in the interval [–2, 2] and discuss the continuity and differentiability in [–2, 2]

Q9

Fill in the blank, statement given below let . The set of points where f (x) is twice differentiable is ……………. .