The solution of the equation using Newton’s Law.

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Exercises Evaluate the following limits. 1. lim cot x/ln x +01x 2. lim x² In x +014 3. lim x* x0+ 4. lim (cos√√x)1/x +014 5. lim x2/(1-cos x) x10 6. lim e*/* 818 7. lim (secx - tan x) x-x/2- 8. lim [1+(3/x)]* x→∞0

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Chapter 2.4, Problem 12E

To determine

The solution of the equation using Newton’s Law.

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Exercises Evaluate the following limits. 1. lim cot x/ln x +01x 2. lim x² In x +014 3. lim x* x0+ 4. lim (cos√√x)1/x +014 5. lim x2/(1-cos x) x10 6. lim e*/* 818 7. lim (secx - tan x) x-x/2- 8. lim [1+(3/x)]* x→∞0

In Exercises 1 through 3, let xo = O and calculate P7(x) and R7(x). 1. f(x)=sin x, x in R. 2. f(x) = cos x, x in R. 3. f(x) = In(1+x), x≥0. 4. In Exercises 1, 2, and 3, for |x| 1, calculate a value of n such that P(x) approximates f(x) to within 10-6. 5. Let (an)neN be a sequence of positive real numbers such that L = lim (an+1/an) exists in R. If L < 1, show that an → 0. [Hint: Let 1111 L

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