Prove the Limit Statement
-The Cross-Sectional Area of a Cylinder $\mathrm { A } = \pi \mathrm { D } ^ { 2 } / 4$

question 41

Multiple Choice

Prove the limit statement
-The cross-sectional area of a cylinder is given by $\mathrm { A } = \pi \mathrm { D } ^ { 2 } / 4$ , where $\mathrm { D }$ is the cylinder diameter. Find the tolerance range of $\mathrm { D }$ such that $| \mathrm { A } - 10 | < 0.01$ as long as $\mathrm { D } _ { \min } < \mathrm { D } < \mathrm { D } _ { \max }$ .

• A) \(\mathrm { D } _ { \min } = 3.567 , \mathrm { D } _ { \max } = 3.578\)
• B) \(\mathrm { D } _ { \min } = 3.567 , \mathrm { D } _ { \max } = 3.570\)
• C) \(\mathrm { D } _ { \min } = 3.558 , \mathrm { D } _ { \max } = 3.570\)
• D) \(\mathrm { D } _ { \min } = 3.558 , \mathrm { D } _ { \max } = 3.578\)

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Definitions:

Market Yield

Market yield refers to the current rate of return anticipated on a bond if held to maturity, factoring in both its price and interest payouts compared to the market's interest rates.

Interest-Rate Sensitivity

The degree to which the price of an investment, often a bond, responds to changes in interest rates.

Bond Prices

The market value of bonds, which inversely fluctuates with interest rates: when rates go up, bond prices fall, and vice versa.

Coupon Rate

The yearly interest rate yielded by a bond, shown as a percent of its nominal value.