67-72. Applying the Intermediate Value Theorema. Use the Intermediate Value Theorem to show that the following equations have a solution on the given interval.70. —x5 - 4x² + 2√x+ 5 = 0; (0, 3)76. T Investment problem Assume you invest $250 at the end of each year for 10 years at an annual interest rate of r.The amount of money in your account after 10 years is given by A(r) =. Assume your goal is250((1+r)¹⁰ − 1)to have $3500 in your account after 10 years.a. Show that there is an interest rate r in the interval (0.01, 0.10) between 1% and 10%-that allows you toreach your financial goal.7

Answered: Use the Intermediate Value Theorem to…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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67-72. Applying the Intermediate Value Theorem
a. Use the Intermediate Value Theorem to show that the following equations have a solution on the given interval.
70. —x5 - 4x² + 2√x+ 5 = 0; (0, 3)
76. T Investment problem Assume you invest $250 at the end of each year for 10 years at an annual interest rate of r.
The amount of money in your account after 10 years is given by A(r) =
. Assume your goal is
250((1+r)¹⁰ − 1)
to have $3500 in your account after 10 years.
a. Show that there is an interest rate r in the interval (0.01, 0.10) between 1% and 10%-that allows you to
reach your financial goal.
7

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Introduction:

The intermediate value theorem asserts that if "f" is a continuous function across a closed interval [a, b] with values $f (a) a n d f (b)$ at its endpoints, then the function takes any value at a point inside the interval that is between the values of $f (a) a n d f (b)$ .