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Jan Hill
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Homework Statement
What must hold true for a function to have a tangent at the origin.
Eg. Given f(x) = 0, x = 0
and f(x0 = xsin (1/x) x does not equal 0
will the graph have a tangent at the origin?
Jan Hill said:Homework Statement
What must hold true for a function to have a tangent at the origin.
Eg. Given f(x) = 0, x = 0
and f(x0 = xsin (1/x) x does not equal 0
will the graph have a tangent at the origin?
Homework Equations
Jan Hill said:What is a finite derivative?
A tangent at the origin is a line that touches a curve at only one point, which is the origin (0,0) on a Cartesian coordinate system.
The tangent at the origin is unique because it is the only tangent that passes through the origin point on a curve. Other tangents may intersect the curve at other points, but not at the origin.
The equation for the tangent at the origin is y=mx, where m is the slope of the tangent line. This equation is derived from the derivative of the curve at the origin.
The tangent at the origin is important in calculus because it helps us understand the behavior of a curve at a specific point. It also allows us to find the slope of the curve at that point, which is essential in determining the rate of change or instantaneous rate of change of a function.
To find the slope of the tangent at the origin, you need to take the derivative of the curve at the origin. This will give you the slope of the tangent line, which can then be plugged into the equation y=mx to find the equation of the tangent line.