Find a simplified form of the difference quotient.Then find the value of the difference quotient
when x = 2 and h = 1. Type only this numerical value.
f(x) = x^2 -1
Solution
f(x) = x^2 -1 => f(x+h) = (x+h)^2 -1 = x^2 + 2xh + h^2 -1
Different quotient = lim h->0 [f(x+h) - f(x)]/h
= lim h->0 [( x^2+2xh+h^2 -1) - (x^2-1) ]/h
= lim h->0 [2xh +h^2]/h
= lim h->0 (2x+h)
= 2x
When h=1 and x=2,
difference quotient = 2x+ h
= (2*2) +1
= 5.
Find a simplified form of the difference quotient.Then find the valu.pdf
1. Find a simplified form of the difference quotient.Then find the value of the difference quotient
when x = 2 and h = 1. Type only this numerical value.
f(x) = x^2 -1
Solution
f(x) = x^2 -1 => f(x+h) = (x+h)^2 -1 = x^2 + 2xh + h^2 -1
Different quotient = lim h->0 [f(x+h) - f(x)]/h
= lim h->0 [( x^2+2xh+h^2 -1) - (x^2-1) ]/h
= lim h->0 [2xh +h^2]/h
= lim h->0 (2x+h)
= 2x
When h=1 and x=2,
difference quotient = 2x+ h
= (2*2) +1
= 5
![Find a simplified form of the difference quotient.Then find the value of the difference quotient
when x = 2 and h = 1. Type only this numerical value.
f(x) = x^2 -1
Solution
f(x) = x^2 -1 => f(x+h) = (x+h)^2 -1 = x^2 + 2xh + h^2 -1
Different quotient = lim h->0 [f(x+h) - f(x)]/h
= lim h->0 [( x^2+2xh+h^2 -1) - (x^2-1) ]/h
= lim h->0 [2xh +h^2]/h
= lim h->0 (2x+h)
= 2x
When h=1 and x=2,
difference quotient = 2x+ h
= (2*2) +1
= 5](https://image.slidesharecdn.com/findasimplifiedformofthedifferencequotient-230402053758-e32ed8ad/85/Find-a-simplified-form-of-the-difference-quotient-Then-find-the-valu-pdf-1-320.jpg)
