Chapter 2: Problem 49
Sine Function Estimate the slope of the curve \(y=\sin x\) at \(x=1 .\) (Hint: See Exercises 41 and $42 . )
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In Exercises \(7 - 14 ,\) determine the limit by substitution. Support graphically. $$\lim _ { x \rightarrow - 4 } ( x + 3 ) ^ { 1998 }$$
Properties of Continuity Prove that if \(f\) is continuous on an interval, then so is \(|f| .\)
Multiple Choice Find the average rate of change of \(f(x)=x^{2}+x\) over the interval \([1,3] .\) . \(\begin{array}{ll}{\text { (A) } y=-2 x} & {\text { (B) } y=2 x \text { (C) } y=-2 x+4} \\ {\text { (D) } y=-x+3} & {\text { (E) } y=x+3}\end{array}\)
In Exercises \(19-22,\) (a) find the slope of the curve at \(x=a\) . (b) Writing to Learn Describe what happens to the tangent at \(x=a\) as \(a\) changes. $$y=\frac{1}{x-1}$$
In Exercises \(31 - 36 ,\) determine the limit. $$\lim _ { x \rightarrow 2 ^ { - } } \operatorname { int } x$$
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