Differentiate : y=(2x^2+1nsqrt (x)) lim _(xarrow 1)(x^3-1)/(x^2)-1 lim _(xarrow 3)((vert x-3vert )/(x-3))

Let's go through each limit step by step.### 1. Differentiate \( y = 2x^2 + \ln(\sqrt{x}) \)First, rewrite the function for easier differentiation: Now, differentiate with respect to : ### 2. Evaluate Factor the numerator and denominator: Cancel the common factor \((x - 1)\): Now, evaluate the limit as : ### 3. Evaluate Consider the definition of the absolute value:- For , - For , \( |x - 3| = -(x - 3) = 3 - x \)Since we are approaching from the right (i.e., ), : For , \( |x - 3| = -(x - 3) \): Since the left-hand limit and the right-hand limit are not equal, the two-sided limit does not exist.### Summary1. The derivative of \( y = 2x^2 + \ln(\sqrt{x}) \) is: 2. The limit is: 3. The limit does not exist because the left-hand limit and the right-hand limit are not equal.