Question

Let f(x) be the function 1/x+5. Then the quotient
f(6+h)−f(6)/h can be simplified to −1/ah+b for:

a= 11

b=

I did all the work to get a but for some reason the number that I keep getting for "B" is wrong

Answer 1

prove d/dx (csc x) = −csc x cot x

Answer 2

First of all , I think you meant f(x) = 1/(x+5)

the difference quotient is
(f(l+h) - f(6))/h
= (1/(11+h) - 1/11 )/h
= (11 - 11 - h)/(11(11+h) (1/h)
= -1 / (11(11+h))

I notice another error is your typing
you probably meant to type:
..... can be simplified to -1/(a(h+b) )

compare -1/(11(11+h)) to -1/(a(h+b))
since we are told a=11, clearly <b>b has to be 11</b> for them to match