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Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
Algebra: direct input of inequalities, implicit polynomials, linear and quadratic equations; calculations with numbers, points and vectors Calculus : direct input of functions (including piecewise-defined); intersections and roots of functions; symbolic derivatives and integrals (built-in CAS); sliders as parameters
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
The slope field can be defined for the following type of differential equations y ′ = f ( x , y ) , {\displaystyle y'=f(x,y),} which can be interpreted geometrically as giving the slope of the tangent to the graph of the differential equation's solution ( integral curve ) at each point ( x , y ) as a function of the point coordinates.
Tangent line at (a, f(a)) In mathematics , a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function ). They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations.
Then, from the differential equation, the slope to the curve at can be computed, and so, the tangent line. Take a small step along that tangent line up to a point A 1 . {\displaystyle A_{1}.} Along this small step, the slope does not change too much, so A 1 {\displaystyle A_{1}} will be close to the curve.
The slope of a linear equation is constant, meaning that the steepness is the same everywhere. However, many graphs such as y = x 2 {\displaystyle y=x^{2}} vary in their steepness. This means that you can no longer pick any two arbitrary points and compute the slope.
Two linear systems using the same set of variables are equivalent if each of the equations in the second system can be derived algebraically from the equations in the first system, and vice versa. Two systems are equivalent if either both are inconsistent or each equation of each of them is a linear combination of the equations of the other one.