To find the limit of lim x → 0 (sin(x)/x) , we start by substituting x = 0 . This gives us: sin(0) /0 = 0 / 0, which is an indeterminate form. Therefore, we need to use a different approach to evaluate this limit. One common method is using L’Hôpital’s Rule, which … Read more
To find the equation of a plane that passes through a given point and is parallel to another plane, we can follow these steps: Identify the Normal Vector: The equation of a plane in the general form is given as Ax + By + Cz = D, where (A, B, C) represents the normal vector … Read more
To evaluate the integral of the function tan(x) * sin(x) * sin(y) with respect to x and y over the specified limits, we need to follow these steps: Understand the function: The function involves a trigonometric identity, and we need to express it in a way that makes integration straightforward. The function can be rewritten … Read more
To simplify the expression 2p4 + 2 + 3 + 5p, we need to combine like terms and arrange the terms in standard form, which is typically ordered from the highest degree to the lowest degree of the variable. Let’s break down the given expression: 2p4 is the term with degree 4. 5p is the … Read more
To find the exact length of the polar curve defined by the equation r = 82 + 0.8θ, we can use the formula for the length of a polar curve. The formula for the length L of a polar curve from an angle θ = a to θ = b is given by: L = … Read more
Triangles are said to be similar if they have the same shape, regardless of their size. According to the angle-angle (AA) criterion for similarity of triangles, if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar. This means that if you can establish that: Angle … Read more
Understanding the Sequence The sequence defined by the formula an = 2n + 3 generates terms based on the value of n. Here, n represents the position of the term in the sequence, and we can calculate individual terms by substituting different values of n. Calculating the Terms Let’s calculate the first 10 terms of … Read more
To find the area under the curve of the function y = 9x³ from x = 1 to x = t, we need to calculate the definite integral of the function over that interval. The formula for the area A under the curve from a to b is given by: A = ∫ab f(x) dx … Read more
To determine how many different combinations of 2 players can be selected from a basketball team consisting of 9 players, we can use the formula for combinations. The formula to calculate combinations is: C(n, r) = n! / (r!(n – r)!) In this case, n is the total number of players (9), and r is … Read more
To find the equation of a line that passes through the point (7, 8) with a slope of 3, we can use the point-slope form of the equation of a line. The point-slope form is given by the formula: y – y1 = m(x – x1) In this formula: (x1, y1) is a point on … Read more