Question

Slope of tangent using lim h approaches 0?

a) ∆y/∆x
b) ∆x/∆y
c) ∆y * ∆x
d) ∆x² + ∆y²

Answer 1

The slope of a tangent line can be found using the limit as h approaches 0. This is typically represented as: lim h->0 [f(x+h) - f(x)] / h. For example, if you have the function y = 2x + 3, the slope of the tangent line at any point on the curve would be 2, which is the coefficient of x.

Step-by-step explanation:

The slope of a tangent line can be found using the limit as h approaches 0. This is typically represented as:

lim h->0 [f(x+h) - f(x)] / h

In other words, you find the difference in y-values for a small change in x, and divide by that small change in x. This represents the instantaneous rate of change at a specific point on a curve. So, the correct answer is:

a) ∆y/∆x

For example, if you have the function y = 2x + 3, the slope of the tangent line at any point on the curve would be 2, which is the coefficient of x.