APM 153 Assignment 10 Solve Blocks, Limits, Derivatives and Integrals, Iterated Sums and
Products.

Answer the following questions on a single Mathcad worksheet. Be sure to write in your
name, APM 153, assignment # and date at the top of the worksheet. Write a header for each problem, (ie "Problem 1 Limits", "Problem 2,..." etc). And then PRINT out your worksheet directly from Mathcad You will turn in your printout and a disk with your worksheet. This assignment will be due at the beginning of the last day of class, on May 1st.

SOLVE BLOCKS

Solve blocks are used to find solutions to related functions. Create a solve block using a "Given"
statement to solve for the roots of the following equations over the range x = -10 to 10.

You wil lfirst have to plot the two functions to determine how many roots there are and to
estimate the approximate x and y values of each root. Use the range x := -10, -9.9... 10 so
that your plot will have smooth curves. Plot the two functions, then set up the solve block!


As you "find" each root, write down the x and y values for each roots in a text region as,...

x y
root1 = 2.1 3.2
root2 = 3.3 1.6

Problem 1. Solve Block - Find all the roots of the two functions between x = -10 to 10

LIMITS

The constant known as Euler's "e" is the base for natural logarithms. Euler's e is a "non-rational" number: that means that it is a non-repeating decimal that does not terminate.

Euler's e is defined as the limit of as x approaches infinity.

Problem 2. Set up a limit to calculate the value of Euler's e, and use your formula to answer the following questions.

A. What is the value of Euler's e if the limit only goes to 4?

B. If x goes to infinity, what result does Mathcad show by default? How can you make MathCad show a numerical result?

DERIVATIVES

Mathcad has two symbols for generating derivatives. When using these symbols, you can try to solve the derivative using either the = to get a numeric answer or you can press CTRL . (the period) to solve symbolically.

Problem 3.1 Given the equation , solve for the first derivative symbolically, and then solve the same equation for the first derivative numerically
when x = 12

Problem 3.2 Given the equation , solve for the second and
third derivatives symbolically. (Hint: you may need to reassign x = x).

INTEGRALS

Use the definite integral operator to solve for the area bounded by the following functions

Problem 4.1 Solve for the area bounded by the two functions within the given range.

Problem 4.2 Solve for the area bounded by all the three functions within the given range.
Hint: there are two regions bounded by all three functions betwee x = 3 and x = 7

ITERATED SUMS

Use the Iterated Sums operator from the calculus toolbar to answer the following questions.

Problem 5.1 What is the sum of all the values of x from x = 50 to x = 10000 ?

Problem 5.2 If f(x) = x + 1/x, what is the sum of all the values of f(x) from x = 1 to x = 100 ?

ITERATED PRODUCTS

Use the Iterated Product operator from the calculus toolbar to answer following question.

Problem 6. Given a freshly shuffled deck of cards, what is the probability of turning
over seven clubs in a row?