Question

solve with explanation

Answer 1

Step-by-step explanation:

• Given if f(x) = x(√x - √x + 1)
• Now we need to find whether at 0 it is continuous or differentiable.
• We need to find the continuity the left hand limit and left hand limit at x = 0 is to be checked. If both are equal then it will be differentiable.
• So f(x) = x(√x - √x + 1)
• Now left hand limit as x tends to 0 minus will be x (√x - √x + 1) as x is negative it will be undefined.
• Now right hand limit as x tends to 0 + will be x(√x - √x + 1)
• Now x >= 0 and x – 1 >=0 by taking range of the function
•                         Or x > = 1
• Therefore left hand limit is not equal to right hand limit.
• Also function is not continuous and also not differentiable.
• Therefore the option none of these holds good.

Reference link will be

https://brainly.in/question/17639251