# Summation notation to infinity

Calc Questions & Answers

1) Make a List of 10 Mathish words or terms that were covered in this Calculus class and provide a brief definition (more than 10 words)

2) If Zero * Infinity is considered Non-Sense, What is Zero divided by Infinity? Give a 25 word or so explanation.

3) Write the sum 2 + 4 + 6 + .....+ 98 + 100 in summation notation.

4) You want to make a tin can using as little material as possible. If the volume of the can is 64 cubic

inches, what should the radius and height of the can equal?

5) A farmer with 750 feet of fencing wants to enclose a rectangular area, and then divide it

into 4 pens with fencing parallel to one side of the rectangle. What is the largest possible

total area of the four pens?

6) Evaluate

Limit |X|

---

X ->0- X

7) A car A is traveling north (up) along the y -axis while a car B is traveling west (to the

left) along the x -axis. At a particular instant, car A is at the point (0, 40) (mi) and traveling

north at 50 mi/hr while car B is at (30,0) and traveling west at 30 mi/hr. At what rate is the

distance between the two cars changing at this instant?

8) What is the asymptote of the curve x+1/x. Write a Mathish expression for the Limit.

9) Write the sum (using summation notation) for the approximation to the area under the curve y = x^3 on the interval [1, 3] using 4 equal subintervals, and using the "midpoint rule". You needn't actually calculate the sum.

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#### Solution Preview

Please see attached for the full solution to the posted problems.

Calc Questions & Answers

1) Make a List of 10 Mathish words or terms that were covered in this Calculus class and provide a brief definition ( more than 10 words)

Answer: Since it is more on your experience in the calculus course, I can just give you suggestions on the words that I know on the Calculus subject.

Differential Calculus - a branch of calculus that deals with the study of the change in the values of a function with respect to the change in the values of an input variable.

Integral Calculus - a branch of calculus that deals with the study of summation of differentials under the function curve.

Summation - it is the process of adding up all the values given.

Limit - it is described as the value of a function as its independent variable reaches a certain point.

Maximum - It is the maximum point of the curve of a function.

Minimum - It is the minimum point of the curve of a function.

Tangent line - it is the line that touches only one point of the given curve.

Asymptote - It is a line or curve that a graph approaches more closely as it approach a certain value of its independent variable.

L'Hôpital's Rule - It is a rule developed to obtain the limit of a rational function. Its limit is equal to the derivative of the numerator divided by the derivative of the denominator substituting the variable's value on the given limit.

Delta - It is a term used to describe a change in value. It is usually equal to the difference between 2 values.

Critical point - It is the point where in the value of the derivative of the function is equal to zero. It indicates either a maximum or a minimum.

Bounded region - it is the region under the curve within certain boundaries. Its area can be computed using integral calculus.

2) If Zero * Infinity is considered Non-Sense, What is Zero divided by Infinity? Give a 25-word or so explanation

Answer: Zero divided by infinity is like . Since approaches the value of zero, it is like zero multiplied by zero. So zero divided by infinity is equal to zero.

3) Write the sum 2 + 4 + 6 + .....+ 98 + 100 in summation notation.

Answer:

4) You want to make a tin can using as little material as possible. If the volume of the can is 64 cubic

inches, what should the radius and height of the can equal?

Answer: We first have to substitute one of the variables to derive a one-variable equation for perimeter.

Then we solve using derivative:

Then we equate it to 0 to get the minimum:

5) A farmer with 750 feet of fencing wants to enclose a rectangular ...

#### Solution Summary

The solution assists with answering calculus questions some regarding the summation notation to infinity.

Summation Notation: Example Problem

I am taking an advanced math course next semester that will involve using summation notation extensively and am somewhat anxious about it.

Could you give me a primer on using Σ single, ΣΣ double, and triple sums with examples?

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