Find \(\ds \lim_{h\to 0}\frac{f(1+h)-f(1)}{h}\) where \(\ds f(x)=\frac{3x+1}{x-2}\text{.}\) What does the result in (a) tell you about the tangent line to the graph ...

In the context of functions, a tangent line refers to a line that touches the graph of a function at exactly one point without crossing it. The equation for calculating tangent lines in this situation ...

In mathematics, the tangent line to a curve at a point is a straight line that touches the curve at this point only. The tangent line can provide valuable insights into the properties of the curve, ...

We can calculate the gradient of a tangent to a curve by differentiating. In order to find the equation of a tangent, we: Differentiate the equation of the curve Substitute the \(x\) value into the ...