What does the limit as h approaches 0 mean?

1 Answer. 1. 2. h is not “one point on the secant line”, it is the horizontal distance between the two points on the secant line. So saying “h goes to 0” means “Let the two points close in on eachother”.

Why do we take h in limits?

Right hand limit means h is approaching 0 from right hand side in number line and left hand limit means h is approaching 0 from left hand side in number line.

What does H 0 represent?

As ‘h’ gets smaller, the value of (x+h) gets closer to (x) and thus f(x+h) gets closer to f(x), and the slope of. the secant line gets closer to the slope of the tangent line at (x). And so as h→0, we get the limit of the. equation at (x) f(x+h)

Why must h go to zero in the definition of the derivative?

The constant never changes—it is constant. Thus, the derivative will always be 0 . Thus, their derivatives are the same—both 2x . When finding the derivative of x2−3 , the −3 can be disregarded since it does not change the way in which the function changes.

What value does this expression approach as h approaches 0?

When h approaches 0, the h’s in this expression will become 0, so that the result is solely dependent on x. We’re talking about the derivative function.

Why is the derivative of a constant 0 and not 1?

The derivative represents the change of a function at any given time. The constant never changes—it is constant. Thus, the derivative will always be 0 . When finding the derivative of x2−3 , the −3 can be disregarded since it does not change the way in which the function changes.

Why is the derivative of a constant 0 Power rule?

Since the derivative is the slope of the function at any given point, then the slope of a constant function is always 0. Hence, the derivative of a constant function is always 0.

What is the meaning of lim h—>0?

Lim h—>0 means the value of h is infinitesimally small. But still it isn’t equal to zero. Value of h can be in two ways. Lim h—>0+, which is called right hand limit and Lim h—>0-, which is called left hand limit.

What is the right hand limit of value h?

Value of h can be in two ways. Lim h—>0+, which is called right hand limit and Lim h—>0-, which is called left hand limit. Right hand limit means h is approaching 0 from right hand side in number line and left hand limit means h is approaching 0 from left hand side in number line.

How do you find the value of E H in math?

Use the definition of e: limh→0(1+h)1/h = e So for small values of h, e ≈ (1+h)1/h, or eh ≈ 1+h. Replace e h in eh−1 h with 1 + h and go on from there.

How to use L’Hopital’s rule to prove E X = E H?

Replace e h in with 1 + h and go on from there. In order to use L’Hopital’s rule, you need to know the derivative of e x, but that’s what the OP is trying to prove. To use L’Hopital’s rule in this case would be circular logic.