Math  /  Calculus

QuestionThis is Section 2.3 Problem 8:8:
For the function f(x)=5xf(x)=\frac{5}{x} (a) A simplified form of the difference quotient f(x+h)f(x)h\frac{f(x+h)-f(x)}{h}, when h0h \neq 0, is \square (b) Use the simplified form to compute the difference quotient for the following. Keep 3 decimal places (rounded). When x=2x=2 and h=0.5h=0.5, the difference quotient is \square When x=2x=2 and h=0.1h=0.1, the difference quotient is \square When x=2x=2 and h=0.01h=0.01, the difference quotient is \square When x=2x=2 and h=0.001h=0.001, the difference quotient is \square

Studdy Solution
Substitute x=2 x=2 and h=0.001 h=0.001 into the simplified difference quotient: 52(2+0.001)=52(2.001)=54.0021.249 \frac{-5}{2(2+0.001)} = \frac{-5}{2(2.001)} = \frac{-5}{4.002} \approx -1.249
Solution: (a) The simplified form of the difference quotient is: 5x(x+h) \frac{-5}{x(x+h)}
(b) The difference quotients for the specified values are: For x=2 x=2 and h=0.5 h=0.5 : 1.000 -1.000
For x=2 x=2 and h=0.1 h=0.1 : 1.190 -1.190
For x=2 x=2 and h=0.01 h=0.01 : 1.243 -1.243
For x=2 x=2 and h=0.001 h=0.001 : 1.249 -1.249

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