Find a simplified form of the difference quotient.Then find the valu.pdf
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The document outlines the process of finding the difference quotient for the function f(x) = x^2 - 1. It includes the steps to simplify the expression and computes the limit as h approaches 0. The final numerical value of the difference quotient when x = 2 and h = 1 is 5.
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![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)
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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