Greeting MHF, first timer here.
I've been taking Calculus over the summer and I've stumbled upon a question that I need assistance with.. Your help is greatly appreciated
DIRECTIONS: Find the equation of the tangent line to the given function at the given point using: limit h->0 (f(x+h)-f(x))/h
Problem: f(x)= sqrt(x-1), (5,2)
What I've done to try and solve this:
Limit h->0 (sqrt(x+h-1) - sqrt (x-1))/h
Then I tried to multiply the numerators conjugate to both the numerator and the denominator so it looks like now (or at least to me):
limit h->0 (x+h-1-x-1)/h(sqrt(x+h-1)+sqrt(x-1))
Then It simplifies to:
limit h->0 (h-2)/h/h(sqrt(x+h-1)+sqrt(x-1))
but when you use direct substitution to find the slope you get -2/0, which isnt possible..
Where have I gone wrong? Any help is greatly appreciated