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Chapter 10: Q. 67 (page 777)

Calculate each of the limits:
$\lim_{h \to 0} \frac{\frac{1}{1 + h} - 1}{h}$ .

Short Answer

Expert verified

The solution for the limit $\lim_{h \to 0} \frac{\frac{1}{1 + h} - 1}{h}$ is $- 1$ .

Step by step solution

01

Step 1. Given Information.

The limit is,

$\lim_{h \to 0} \frac{\frac{1}{1 + h} - 1}{h}$ .

02

Step 2. Finding the solution.

$\lim_{h \to 0} \frac{\frac{1}{1 + h} - 1}{h} = \lim_{h \to 0} \frac{\frac{1 - 1 - h}{1 + h}}{h} = \lim_{h \to 0} \frac{- h}{h (1 + h)} = \lim_{h \to 0} \frac{- 1}{1 + h}$

Inputting $h = 0$ ,

$= \frac{- 1}{1 + 0} = \frac{- 1}{1} = - 1$

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Most popular questions from this chapter

In Exercises 36–41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

$P (4, - 2), Q (- 2, 0), R (1, - 5)$

(Hint: Think of the $x y$ -plane as part of $ℝ^{3}$ .)

In Exercises 22–29 compute the indicated quantities when $u = (2, 1, - 3), v = (4, 0, 1), and w = (- 2, 6, 5)$

$v \times w and w \times v$

In Exercises 30–35 compute the indicated quantities when $u = (- 3, 1, - 4), v = (2, 0, 5), and w = (1, 3, 13)$

Find the area of the parallelogram determined by the vectors u and v.

Find $u + v a n d u - v$ also sketch $u, v, u + v, u - v$

$u = (4, 0) a n d v = (0, 3)$

A function f that satisfies the hypotheses of Rolle’s Theorem on [−2, 2] and for which there are exactly three values c ∈ (−2, 2) that satisfy the conclusion of the theorem .

See all solutions

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