Master this deck with 21 terms through effective study methods.
Generated from uploaded pdf
The trigonometric form of a complex number Z can be expressed as Z = r(cos θ + i sin θ), where r is the modulus and θ is the argument. To find this form, calculate the modulus and argument based on the real and imaginary parts.
To find the number of terms in the expansion of (x + y)^(n) that contains x^6y^18, use the formula for the binomial expansion. The number of terms is given by n + 1, where n is the sum of the exponents of x and y.
To find the coordinates of point C, set the distances from C to A and C to B equal to each other. Since C lies on the Y-axis, its coordinates will be (0, y, 0). Solve for y to find the specific coordinate.
The first derivative of the function y = ln(x) is given by y' = 1/x, where x > 0.
If the absolute maximum value of a function equals -2, it indicates that the highest point on the graph of the function does not exceed -2. This can occur in functions that are decreasing or have a maximum point at that value.
To find the equation of a straight line that passes through a point (x0, y0, z0) and is parallel to another line, use the direction vector of the given line and the point-slope form of the line equation.
The integral of 1/x with respect to x is ln|x| + C, where C is the constant of integration.
The surface area of triangle OAB can be calculated using the formula for the area of a triangle, which is 1/2 * base * height. The base and height can be determined from the points where the tangent intersects the axes.
The principle amplitude of a complex number is the angle θ in the polar form r(cos θ + i sin θ). It can be found using the arctangent function: θ = arctan(imaginary part / real part).
To differentiate f(x) = sec(x)(cos(x) + sin(x)), apply the product rule and the chain rule, taking into account the derivatives of sec(x), cos(x), and sin(x).
The equation of a plane that passes through a point (x0, y0, z0) and is parallel to the x and y axes can be expressed as z = z0.
Vectors in the same plane can be added or subtracted to find resultant vectors. The relationship can be expressed using vector addition and scalar multiplication.
To solve the equation (y-1)y'' = k(y')^2 for k, rearrange the equation to isolate k and express it in terms of y, y', and y''.
The absolute maximum value in a function's interval indicates the highest point the function reaches within that interval, which is crucial for understanding the function's behavior and optimization.
To find the tangent line to a curve at a given point, calculate the derivative of the function at that point to find the slope, then use the point-slope form of the line equation.
The area of a triangle given its vertices can be calculated using the formula: Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|.
The tangent to a curve at a point represents the instantaneous rate of change of the function at that point, providing insight into the function's behavior.
The number of terms in a binomial expansion (a + b)^n is given by n + 1, where n is the exponent.
The coordinates of points A, B, and C in a 3D space can be analyzed using distance formulas and geometric properties to determine relationships such as collinearity or equidistance.
The derivative of ln(x^2) can be found using the chain rule, resulting in 2/x.
A complex number can be expressed in polar form as r(cos θ + i sin θ), where r is the modulus and θ is the argument, calculated using the real and imaginary parts.