Use the formula for instantaneous rate of change, approximating the limit by using smaller and smaller values of hh , to find the instantaneous rate of change for each function at the given value. f(x)=x^{x} at x=2

Step-by-step explanation:

Given

at

Required

The instantaneous rate of change

We have:

The instantaneous rate of change is:

implies that:

So, we have:

Keep reducing h but set a constant at 2

Notice that:

for and

Hence, the instantaneous rate of change is:

---- approximated

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .