Question

lim(h→0)(f(x+2h)-f(x))/h)​

Answer 1

Answer:

I am not able to understand this

Step-by-step explanation:

Answer 2

Answer:

Show

lim

h→ 0

f(x+2h)−2f(x+h)+f(x)

h2

=f″(x)

Proof:

By definition:

f′(x)=

lim

h→ 0

f(x+h)−f(x)

h

Using this idea it would imply:

1) f″(x)=

lim

h→ 0

f′(x+h)−f′(x)

h

As such it is required that I find an expression for f′(x+h). This is where I'm not sure if the step I took is legitimate.

An expression for f′(x+h) is:

f′(x+h)=

lim

h→ 0

f(x+2h)−f(x+h)

h

Combining this with the definition of f′(x) and inserting it into 1) you arrive at:

lim

h→ 0

f(x+2h)−2f(x+h)+f(x)

h2

=f″(x)