𝕖𝕕𝕦𝕔𝕒𝕥𝕚𝕠𝕟 ️️️𝕗𝕠𝕣 𝕒𝕝𝕝 📚

## 1. Understanding Power Functions Question: 1 Which one of the following functions is NOT a power function? * A. f(x) = x^{-3/5} * B. f(x) = \sqrt{2}x^2 * C. f(x) = \pi x^5 * D. f(x) = (\sqrt{3})^x Explanation: A power function is defined as a function of the form f(x) = ax^n, where a and n are fixed real numbers (a is the coefficient, n is the exponent). In a power function, the variable (x) is the base, and the exponent is a constant. * In A, B, and C, the variable x is the base, and the exponent is a constant number. Therefore, they are power functions. * In D, f(x) = (\sqrt{3})^x, the variable x is in the exponent position, not the base. This is defined as an exponential function, not a power function. Correct Answer: D ## 2. Calculating the Derivative Question: Let f(x) = (1 - 2x)^{1/2}. What is the value of f'(x)? * A. \frac{1}{\sqrt{1-2x}} * B. -\frac{1}{2}\sqrt{1-2x} * C. \frac{1}{2}\sqrt{1-2x} * D. \frac{-1}{\sqrt{1-2x}} Explanation: To solve this, we use the Chain Rule. The chain rule states that if f(x) = g(h(x)), then f'(x) = g'(h(x)) \cdot h'(x). 1. Identify the outer function g(u) = u^{1/2} and the inner function u = (1 - 2x). 2. Take the derivative of the outer function: \frac{d}{du}(u^{1/2}) = \frac{1}{2}u^{-1/2} = \frac{1}{2\sqrt{u}}. 3. Take the derivative of the inner function: \frac{d}{dx}(1 - 2x) = -2. 4. Multiply them together:    Correct Answer: D ## 3. Scalar vs. Vector Quantities Question: Which of the following statements describes the difference between scalar and vector quantities? * A. Physical quantities that only have direction are scalars, while that have only magnitude are vectors. * B. Physical quantities that only have magnitude are scalars, while that have both magnitude and direction are vectors. * C. Physical quantities that only have magnitude are vectors, while that have both magnitude and direction are scalars. * D. Physical quantities that only have direction are vectors, while that have both magnitude and direction are scalars. Explanation: To distinguish between these two fundamental physical quantities, remember these definitions: * Scalar Quantities: Have only magnitude (size or amount). Examples include mass, time, distance, and temperature. * Vector Quantities: Have both magnitude AND direction. Examples include displacement, velocity, force, and acceleration. Comparing this to the options, Option B correctly matches these definitions. Correct Answer: B የሚቀጥለው ክፍል እንዲለቀቅ 👍 Like እና Share በማድረግ ለጓደኞቻችሁ አጋሩ!