Chapter 13: Q 4. (page 1014)

Let $R = {(x, y) ∣ a \leq x \leq b and c \leq y \leq d}$ be a rectangular region. Explain why R is both a type I region and a type II region.

Short Answer

Expert verified

The region may be considered as either type I or type II region.

Step by step solution

Given Information

It is given that $R = {(x, y) ∣ a \leq x \leq b and c \leq y \leq d}$

Determining type I region

It is observed that for values of $x$ in $[a, b]$ , the function $y = c$ and $y = d$ are such that $c < d$

Hence, region is bounded by $y = c, above by y = d,$ left by $x = a$ and right by $x = b$

Region is type I.

Determining type II region

For all values of $y$ in interval $[c, d]$ , the functions $x = a, x = b$ are such that $a < b$ .

Hence, region is bounded below by $y = c, above by y = d,$ left by $x = a$ and right by $x = b$

Region is type II region.

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Let $R = {(x, y) ∣ a \leq x \leq b and c \leq y \leq d}$ be a rectangular region. Explain why R is both a type I region and a type II region.

Short Answer

Step by step solution

Given Information

Determining type I region

Determining type II region

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Let R={(x,y)∣a≤x≤bandc≤y≤d}be a rectangular region. Explain why R is both a type I region and a type II region.

Short Answer

Step by step solution

Given Information

Determining type I region

Determining type II region

One App. One Place for Learning.

Most popular questions from this chapter

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Mechanics Maths

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Let $R = {(x, y) ∣ a \leq x \leq b and c \leq y \leq d}$ be a rectangular region. Explain why R is both a type I region and a type II region.