Example Question - value of a
Here are examples of questions we've helped users solve.
Determining the Value of a for Curves Intersection
Langkah 1: Susun persamaan f(x) = h(x) dan g(x) = h(x). Langkah 2: Selesaikan untuk x dari kedua persamaan tersebut. Persamaan f(x) = h(x): -2x^2 + 1 = -5x^2 + 1 3x^2 = 0 x = 0 Persamaan g(x) = h(x): -2x^2 + 1 = -ax^2 + 1 2x^2 - ax^2 = 0 x^2(2 - a) = 0 Sebab x tidak boleh sentiasa 0 (asta yang akan jadi jika kita bawa 2 - a = 0), maka 2 - a = 0 a = 2 Langkah 3: Tentukan julat nilai a. Kerana tiada pembatasan lain yang diberikan, kita boleh simpulkan bahawa nilai a mesti 2 untuk memastikan semua kurva bersilang pada titik yang sama.
Finding Value of 'a' for Continuous Function at x = 2
The function \( f(x) \) is defined by three expressions for different ranges of \( x \), and we are asked to find the value of "a" given that the function is continuous at \( x = 2 \). For a function to be continuous at a point, the left-hand limit (as \( x \) approaches the point from the left), the right-hand limit (as \( x \) approaches the point from the right), and the function's value at the point must all be the same. Let's evaluate the limit from the left (\( x < 2 \)) and from the right (\( x > 2 \)) as well as the function's value at \( x = 2 \): - The right-hand limit as \( x \) approaches 2 from the right is given by the expression \( x + a \). As \( x \) approaches 2, this expression becomes \( 2 + a \). - The function's value at \( x = 2 \) is given as 5. - The left-hand limit as \( x \) approaches 2 from the left is given by the expression \( 2x + 1 \). As \( x \) approaches 2, this expression becomes \( 2(2) + 1 = 4 + 1 = 5 \). Since the function is continuous at \( x = 2 \), the right-hand limit must equal the left-hand limit and also the function's value at \( x = 2 \). So we have the equation \( 2 + a = 5 \). Solving for \( a \): \[ a = 5 - 2 \] \[ a = 3 \] Therefore, the value of "a" that makes the function continuous at \( x = 2 \) is 3.
Determination of Quadratic Expression Coefficient
The general form of a quadratic expression is \( ax^2 + bx + c \). Given the quadratic expression \( 4 - 3x - 2x^2 \), we need to compare this with the general form to find the value of \( a \). First, rearrange the given expression to match the general form: \( -2x^2 - 3x + 4 \) Now, we can see that \( a \), the coefficient of \( x^2 \), is \( -2 \). Therefore, the value of \( a \) is \( -2 \), which corresponds to option C.
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