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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
Time
5 mins
Type
Multiple Choice
Quiz #
9,524
Updated
Dec 03 21
# Qns
5
Difficulty
Impossible
Avg Score
1 / 5
Plays
3683
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Question 1 of 5
1. What is the limit as x approaches 0 of (2x^3 +10x) / ( 5x^3 + 2x^2 + 7x) ? Hint

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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

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Question 3 of 5
3. Find the length of the curve (x^4 + 75)/(30x) from x=1 to x=6 Hint

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Question 4 of 5
4. What is the limit as x approaches infinity of (1 + (k/x))to the x? Hint

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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

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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) ?

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

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

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?