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High School Calculus Trivia Quiz

High School Calculus. Calculators are permitted provided that it is not programmable and without graphic display. But I can't do anything if you use it, can I? lol. Feel free to contact me to comment on the quiz.

A multiple-choice quiz by ff7rule. Estimated time: 5 mins.

Author
ff7rule

Time
5 mins

Type
Multiple Choice

Quiz #
9,524

Updated
Dec 03 21

# Qns
5

Difficulty
Impossible

Avg Score
1 / 5

Plays
3681

One at a Time - Single Page - Timed Game

Question 1 of 5

1. What is the limit as x approaches 0 of (2x^3 +10x) / ( 5x^3 + 2x^2 + 7x) ? Hint

7/10

10/7

2/5

5/2

NEXT>

Question 2 of 5

2. Find the area between the function 1/(x-1)^2 and the x-axis between x = -8 and x = 10 Hint

infinity

NEXT>

Question 3 of 5

3. Find the length of the curve (x^4 + 75)/(30x) from x=1 to x=6 Hint

21/16

21/4

37/4

37/16

NEXT>

Question 4 of 5

4. What is the limit as x approaches infinity of (1 + (k/x))to the x? Hint

ln(k)

pi to the k

e to the k

infinity to the k

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Question 5 of 5

5. What is the 100th derivative of ((sin(2x))squared) with respect to x when x = 1 plus the 100th derivative of (cos(2x))squared) with respect to x when x = 1? Hint

-1

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Quiz Answer Key and Fun Facts

1. What is the limit as x approaches 0 of (2x^3 +10x) / ( 5x^3 + 2x^2 + 7x) ?

Answer: 10/7

Apply l'hopital's rule.. you'll get 6x squared + 10 over 15x squared + 4x + 7. Subbing in zero, you get 10 over 7 or 1.428571428571 (L'hopital's rule)

2. Find the area between the function 1/(x-1)^2 and the x-axis between x = -8 and x = 10

Answer: infinity

You must first see that the asymtote x=1 is between the left and right boundary. Thus you must separate the integrals to 1) the limit of integral of f(x) between -8 and a as a approaches 1 from the left and 2) the limit of the integral of f(x) between a and 10 as a approaches 1 from the right. The both integrals turn out to be infinity, thus the answer is infinity. (Improper Integrals)

3. Find the length of the curve (x^4 + 75)/(30x) from x=1 to x=6

Answer: 37/4

Use the arc length formula.. Integral from a to b of sqrt(1 + (y')squared) where y' is the derivative of the function. (Arc Length)

4. What is the limit as x approaches infinity of (1 + (k/x))to the x?

Answer: e to the k

Proof requires l'hopital's rule and e to the ((1 + (k over x))to the x) There may be other proofs. (Logarithms and Exponential Functions)

5. What is the 100th derivative of ((sin(2x))squared) with respect to x when x = 1 plus the 100th derivative of (cos(2x))squared) with respect to x when x = 1?

Answer: 0

First you must group the two derivatives. Then the question becomes 'what is the 100th derivative of ((sin(2x))squared + (cos(2x))squared) when x = 1. Since (sin(2x))squared + (cos(2x))squared) = 1 the first derivative is 0, and on and on... thus the 100th derivative is 0, regardless of x value. Feel free to contact me to comment on the quiz.

Source: Author ff7rule

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