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To find the linearization L(x) of the function f(x) = x^4 + 2x^2 + x + 1 at a specific point, we will follow these steps: Choose the point of linearization: Let’s assume we want to find the linearization at the point a. For example, let’s take a = 0. Compute the function value: Calculate … Read more

The conversion between miles and kilometers is a common question for travelers and those who might be curious about distance measurements. A mile is equivalent to approximately 1.60934 kilometers. This means that whenever you hear someone say they traveled a mile, you can convert that to kilometers by multiplying by 1.60934. For example, if you … Read more

To determine the possible lengths of the third side of a triangle when two sides measure 5 inches and 12 inches, we can apply the triangle inequality theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Given … Read more

The zeros of a function are the points where the graph intersects the x-axis, which means the output of the function (y) is zero. To find the zeros of the function y = x^3 + 3x^2 – 4, we need to set the equation equal to zero and solve for x: x^3 + 3x^2 – … Read more

To find the combined function fx(gx), we start with the two given functions: 1. fx: fx(x) = x2 + 3x + 4 2. gx: gx(x) = x + 5 First, we will substitute gx(x) into fx(x). This means wherever we see an x in the function fx, we will replace it with gx(x). Let’s proceed … Read more

To find the value of f(1), we need to substitute x = 1 into the function f(x) = 3x + 4. Here’s how we do it step by step: Substitute 1 for x in the function: f(1) = 3(1) + 4. Simplify the equation: f(1) = 3 + 4. Perform the addition: f(1) = 7. … Read more

To find the general solution of the differential equation given by x2y – xy + 4 = 0, we can start by reorganizing the equation. The equation can be rewritten as: x2y – xy = -4 Next, we can factor out a common term from the left-hand side: y(x2 – x) = -4 Now, solving … Read more

To calculate the circumference of a circle, you can use the formula: C = π × D where C is the circumference and D is the diameter. Since the diameter of the circle is 6 yards, we can substitute that value into the equation: C = π × 6 yards Now, using the approximate value … Read more

To find a polar equation corresponding to the Cartesian equation xy = 1, we start by recalling the relationships between Cartesian and polar coordinates. In polar coordinates, x and y can be expressed as: x = r imes ext{cos}( heta) y = r imes ext{sin}( heta) Here, r is the radial distance from the origin, … Read more