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The general equation for a linear approximation is f(x) ≈ f(x0) + f'(x0)(x-x0) where f(x0) is the value of the function at x0 and f'(x0) is the derivative at x0. This describes a tangent line used to approximate the function.
In higher order functions, the same concept can be applied. f(x,y) ≈ f(x0,y0) + fx(x0,y0)(x-x0) + fy(x0,y0)(y-y0) where f(x0,y0) is the value of the function at (x0,y0), fx(x0,y0) is the partial derivative with respect to x at (x0,y0), and fy(x0,y0) is the partial derivative with respect to y at (x0,y0). This describes a tangent plane used to approximate a surface.
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How can you tell if a linear appoximation is too large or too small?
The precision of a linear approximation is dependent on the concavity of the function. If the function is concave down then the linear approximation will lay above the curve, so it will be an over-approximation ("too large"). If the function is concave up then the linear approximation will lay below the curve, so it will be an under-approximation ("too small").
What does the graph of the equation 2x-3y equals 6 look like?
The equation 2x - 3y = 6 is a linear equation and a linear equation is always has a straight line as a graph
Is x plus 3xy equals 9 a linear equation?
no
Is y equals x2 plus 2 a linear equation?
No, y=x^2 + 2 is a quadratic equation. A linear equation is one in the form y=mx+b. A quadratic has a form y=ax^2+bx+c.
3s equals 2t is this a linear equation or nonlinear?
3s=2t can also be written as 3y=2x or 3x=2y. Either way, it is linear. To find out if it is linear, simply graph it. If you can draw a completely vertical line through any point of the graph without intersecting more than one point of the graph, then it is linear. This equation (3s=2t), it is linear.
