The expression : lim h--> 0 (√h+9 -3)/ h represents the slope of the tangent of some

function y = f(x) at x =4.

Determine the functions y = f(x)

Determine the numeric value of lim h--> 0 (√h+9 -3)/ h

3 answers

y = f(x)
slope at x = [f(x+h) - f(x) ] /h as h -->0
What you typed makes no sense. Perhaps you mean
lim h--> 0 [ √ (h+9) - 3 ] / h at x = 4
looks like f(4) = 3
√ (h+9) = (9+h)^1/2 = 3 + (1/2)(1/3)h +(1/2)(-1/2)/2 *(1/2)^-1.5 h^2 ....
(binomial series)
so as h approaches 0
[ 3 + 1/6 h + ..... - 3 ] /h = 1/6 h /h = 1/6
sorry for the poor wording.

The expression : lim [√(h+9) -3]/ h as h --> 0 represents the slope of the tangent of some function f(x) when x = 4.

How do you determine the function f(x)?
Opps again. I meant to say:

Determine the function f(x)