Consider the following for the two items that follow: Let the function f(x) = x2 + 9
\[ \lim_{x \to 0} \frac{\sqrt{f(x)} - 3}{\sqrt{f(x) + 7} - 4} \]
2/3
Using limits and simplifying the expression, we get 2/3.
The non-negative values of \(b\) for which the function \(\frac{16x^3}{3} - 4bx^2 + x\) has neither maximum nor minimum in the range \(x > 0\) is
A wire of length 20 cm is to be bent into a rectangle. Which of the following statements is/are correct?
I. The rectangle of the largest area is the square.
II. It is possible to form a rectangle of an area of \(27 \, \text{cm}^2\).
Select the answer using the code given below.
Four small squares of side x are cut out of a square of side 12 cm to make a tray by folding the edges. What is the value of x so that the tray has the maximum volume?
The maximum value of 5 + 20x - 4x², when x is a real number is
If 3 ≤ x ≤ 10 and 5 ≤ y ≤ 15 , then maximum value of \(\left(\frac{x}{y}\right)\) is-