QUESTION 1

Exercise 1:
Use a graph of (x−2)²=4sin(x) to find solutions to the equation valid to 2 decimal points:
enter the roots…

QUESTION 2

1. Exercise 2:

   Use the zooming technique to find solutions of 50 + sin(x) = 2x

   which are valid to at least two decimal places.

   Hint: Try to estimate the value of 50 + sinx. This will give you an idea in which x interval are the possible solutions!
   enter a number…

QUESTION 3

Exercise 3a:
Folklore is that exponential functions grow faster than polynomial functions. Although true, you need to be careful about how you interpret this statement, as this exercise shows.
Consider the functions z₁=e^x and z₂=x⁴. Plot them together on the interval [0,4].

• From their graphs, how can you determine which graph is the exponential and which is the polynomial

QUESTION 4

1. Exercise 3b:
   Find the value of x (to two decimal places) for the point of intersection by zooming on the zero of f(x)=e^x−x⁴. (or by zooming on the intersection point of the functions z₁=e^x, z₂=x⁴.)

QUESTION 5

1. Exercise 3c:
   On this graph, x⁴ is larger than e^x from the intersection point to x=4. Experiment to determine how large a value of x is needed for the exponential to catch up to x⁴. Then find the

   second intersection point. (correct to three decimal places.) This one is larger than 4. In fact, you now have found two intersection points (x₁, y₁), (x₂, y₂). (where x₁ < x₂) Up to x₁ the

   function e^x is bigger, from x₁ to x₂ the function x⁴ is the bigger. What happens after x₂?

   What is the x-coordinate of the second intersection point?

   enter a number…

6 points  

QUESTION 6

1. Exercise 3d:

   What happens to the behavior of z₁ and z₂ after the second intersection point?

DETAILED ASSIGNMENT

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