Question

x + h - V
Evaluate : lim
h→0
h​

Answer 1

Answer:

Step-by-step explanation:

Also known as: (Definition of Limit), and (Increment definition of derivative)

f ’(x) = lim f(x+h) – f(x)

h→0 h

This equation is essentially the old slope equation for a line:

2 1

2 1

x x

y y m −

− =

f (x+h) – represents (y2)

f (x) – represents (y1)

x – represents (x1)

x + h − represents (x2)

h – represents the change in x or (x2 – x1) or ∆x

f (x+h) – f (x) – represents (y2 – y1)

Lim – represents the slope M as h→0

2 1

2 1

x x

y y M −

− = x h x

f x h f x

+ −

+ − = ( )

( ) ( )

h

f (x + h) − f (x) =

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)

f(x)

x x+h

h

f(x) = 2(x – 4)

2