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Quiz about Calculus Fun or My Head Hurts
Quiz about Calculus Fun or My Head Hurts

Calculus Fun (or My Head Hurts!) Quiz


This quiz is based on infinitesimal calculus (specifically single-variable). It involves the history, definitions, and some problems to solve. Good luck!

A multiple-choice quiz by hausc018. Estimated time: 4 mins.
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Author
hausc018
Time
4 mins
Type
Multiple Choice
Quiz #
335,741
Updated
Dec 03 21
# Qns
10
Difficulty
Average
Avg Score
7 / 10
Plays
781
Last 3 plays: BarbaraMcI (6/10), 1nn1 (10/10), Guest 71 (7/10).
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Question 1 of 10
1. What is the broadest definition of calculus?
Hint


Question 2 of 10
2. What are the two main branches of calculus?

Hint


Question 3 of 10
3. Who is widely considered to be the father of calculus (or the father of differential and integral calculus)? Hint


Question 4 of 10
4. When differentiating a function, what does the answer mean? In other words, what does the derivative of a function represent? Hint


Question 5 of 10
5. When integrating a function, what does the answer mean? In other words, what does the integral of a function represent? Hint


Question 6 of 10
6. What does it mean to find the limit of a function? Hint


Question 7 of 10
7. Consider 'x' to be a variable. What is the derivative of 12x^4 + 10x^3 - 5x^2 + 16 with respect to x? Hint


Question 8 of 10
8. Consider 'x' to be a variable. What is the integral of 18x^2 - 10x + 3 with respect to x? Pick the most correct solution. Hint


Question 9 of 10
9. Suppose the integral was already performed on an equation. What is the simplified answer if you now take the integral from 0 to 1 for the following integrated equation:

8x^3 + 3x^2 - 4x + C

(Hint: closed interval [a=0, b=1])
Hint


Question 10 of 10
10. Which of the following is not a known series used in calculus? Hint



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Most Recent Scores
Sep 30 2024 : BarbaraMcI: 6/10
Sep 07 2024 : 1nn1: 10/10
Aug 17 2024 : Guest 71: 7/10
Aug 14 2024 : CageyCretin: 4/10

Score Distribution

quiz
Quiz Answer Key and Fun Facts
1. What is the broadest definition of calculus?

Answer: the study of change

Calculus involves many other components when defining it, but in general it is the study of change. The study of operations and applications is algebra. The study of shape is geometry. The study of collections of data is statistics.
2. What are the two main branches of calculus?

Answer: differential and integral

The Fundamental Theorem of Calculus relates the two branches by stating they are inverse operations of each other.
3. Who is widely considered to be the father of calculus (or the father of differential and integral calculus)?

Answer: Both

Today, they both share credit for developing differential and integral calculus. It has long been disputed as to who actually developed it first. Leibniz developed infinitesimal calculus independently and published his work first, but Newton began work on it before and took many years to publish his work. Leibniz focused more on systematic ways to solve problems and came up with appropriate symbols while Newton came up with rules, series, and functions in general.
4. When differentiating a function, what does the answer mean? In other words, what does the derivative of a function represent?

Answer: both

The answer is both because there are two ways in defining the derivative of a function: physically and geometrically. The most common forms of differential notation are Leibniz notation, which is noted as dy/dx and the Legrange notation or prime notation, which is noted as f'(x). Both notations are defined as the derivative of y with respect to x.
5. When integrating a function, what does the answer mean? In other words, what does the integral of a function represent?

Answer: the area under the graph of a funtion bounded by a closed interval [a,b]

Essentially, an integral is the anti-derivative. It is solved by taking the anti-derivative of the function with respect to x from the closed interval 'b' and subtracting the anti-derivative of the function with respect to x from the closed interval 'a'.
6. What does it mean to find the limit of a function?

Answer: the behavior of a function as it approaches a specific input

When determining the limit of a function, you are seeing what value (if any) the function is as it approaches a specific input. The limit may approach a constant, but it may also approach infinity or zero. Depending on the function, it may not even exist in either case.
7. Consider 'x' to be a variable. What is the derivative of 12x^4 + 10x^3 - 5x^2 + 16 with respect to x?

Answer: 48x^3 + 30x^2 - 10x

The formula for finding a derivative of a single-variable equation is:

f'(x) = (y*C)x^y-1, where C is a constant

Therefore, the answer is obtained by applying the formula in this way:

(4*12)x^4-1 + (3*10)x^3-1 - (5*2)x^2-1 + (0*16)

= 48x^3 + 30x^2 - 10x
8. Consider 'x' to be a variable. What is the integral of 18x^2 - 10x + 3 with respect to x? Pick the most correct solution.

Answer: 6x^3 - 5x^2 + 3x + C

The formula for finding an integral of a single-variable equation is:

F(x) = (Bx^y+1)/(y+1) + C, where B, C are constants

Therefore, the answer is obtained by applying the formula in this way:

(18x^2+1)/(2+1) - (10x^1+1)/(1+1) + (3x^0+1)/(0+1) + C

= (18x^3)/3 - (10x^2)/2 + (3x)/1 + C

= 6x^3 - 5x^2 + 3x + C
9. Suppose the integral was already performed on an equation. What is the simplified answer if you now take the integral from 0 to 1 for the following integrated equation: 8x^3 + 3x^2 - 4x + C (Hint: closed interval [a=0, b=1])

Answer: 7

To simplify the integral from 0 to 1, use this formula:

F(x) = F(b) - F(a), where a and b are the bounds (in this case, a=0 and b=1)

Therefore, the answer is obtained by applying the formula in this way:

[8x^3 + 3x^2 - 4x + C]0-->1

= [8(1) + 3(1) - 4(1) + C] - [8(0) + 3(0) - 4(0) + C]

= [8 + 3 - 4 + C] - [0 + 0 - 0 + C]

= [7 + C] - [C]

= 7
10. Which of the following is not a known series used in calculus?

Answer: Simpson's Rule

A series is the sum of the terms in a sequence and can be definite or indefinite. Simpson's Rule is used to approximate definite integrals, not series.
Source: Author hausc018

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