\( 2.3 x=3+\sqrt{x^{2}+y^{2}} \) 2.3.1. 2.3.2 Determine \( \frac{d y}{d x} \) Determine the equation of the tangent to the graph at point \( (4,3 \)

\( f(x)=3 x^{2}+6 x-45 \) A. The parabola opens downward and has a maximum value of -48 . B. The parabola opens upward and has a minimum value of (c) What is the range of \( f(x) \) ? The range of \( f(x) \) is \( [-48, \infty) \). (Type your answer in interval notation. Use integers or fractions for any nungibers in the expression.) (d) On what interval is the function increasing? The function is increasing on \( (-1, \infty) \). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) On what interval is the function decreasing? The function is decreasing on \( \square \). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

BÀI TẬP Bài 1. Xác định cận lấy tích phân trong hệ tọa độ cực của tích phân: \( I=\iint_{D} f(x ; y) d x d y \) với miền \( D=\left\{(x ; y) \mid x^{2}+y^{2}-2 x \leq 0 ; y \leq 0\right\} \)

(a) Prove that the set of natural numbers is countable. (b) Find the limit point/points of: \( \mathrm{A}=\left\{1,-1,1 \frac{1}{2},-1 \frac{1}{2}, 1 \frac{1}{3},-1 \frac{1}{3}, \ldots\right\} \)

If \( g(x) = e^{2x} \), find \( g(3) \).

Hallar \( y_{1} \) \( y=\frac{x^{2}}{\sqrt[3]{x^{2}+4}} \)