let f(x)=sqrt x+4. Calculate the difference quotient f(5+h)-f(5)/h for
h=.1
h=.01
h=-.01
h=-.1
To find the difference quotient, we need to substitute the values of f(x) and h into the given formula:
The given function is f(x) = sqrt(x) + 4.
For h = 0.1:
f(5 + h) - f(5) = [sqrt(5 + 0.1) + 4] - [sqrt(5) + 4]
= [sqrt(5.1) + 4] - [sqrt(5) + 4]
= sqrt(5.1) - sqrt(5)
Therefore, the difference quotient for h = 0.1 is: [sqrt(5.1) - sqrt(5)] / 0.1
For h = 0.01:
f(5 + h) - f(5) = [sqrt(5 + 0.01) + 4] - [sqrt(5) + 4]
= [sqrt(5.01) + 4] - [sqrt(5) + 4]
= sqrt(5.01) - sqrt(5)
Therefore, the difference quotient for h = 0.01 is: [sqrt(5.01) - sqrt(5)] / 0.01
For h = -0.01:
f(5 + h) - f(5) = [sqrt(5 - 0.01) + 4] - [sqrt(5) + 4]
= [sqrt(4.99) + 4] - [sqrt(5) + 4]
= sqrt(4.99) - sqrt(5)
Therefore, the difference quotient for h = -0.01 is: [sqrt(4.99) - sqrt(5)] / -0.01
For h = -0.1:
f(5 + h) - f(5) = [sqrt(5 - 0.1) + 4] - [sqrt(5) + 4]
= [sqrt(4.9) + 4] - [sqrt(5) + 4]
= sqrt(4.9) - sqrt(5)
Therefore, the difference quotient for h = -0.1 is: [sqrt(4.9) - sqrt(5)] / -0.1
Please note that these values can be further simplified.