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1-23 Game Night Flashcards | StudBud
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1-23 Game Night
1-23 Game Night
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Answers
1
Evaluate the limit:\lim_{v\rightarrow0}\left[\frac{av^2+bv}{v}\right]
a
indeterminate
a+b
b
2
What do you call functions with operations that are not addition, subtraction, multiplication, and power?
Transcendental Functions
Cartesian Functions
Elementary Functions
Algebraic Functions
3
What is the domain of the function f\left(x\right)=\sqrt{x-1}-\ln\left(x+2\right)?
x can be any real number.
x should be between -2 and 1, including 1.
x should be greater than -2.
x should be greater than or equal to 1.
4
One of the Fathers of Calculus is Isaac Newton. What we now call "derivative" is termed as what in his calculus?
PSEUDO-SLOPE
FLUXION
GRADIENT
TANGENT
5
For higher-order derivatives written in the prime notation, instead of apostrophes, which of the following is used?
Roman numerals
Subscripts
Superscript indicating only the number of times the derivative was took
Dots on top of the variable
6
\lim_{x\rightarrow0}\left[\frac{A}{m+n^{\frac{1}{x}}}\right], where A, m, and n are constants.
+\infty
does not exist
\frac{A}{m+n}
0
7
If f\left(g\left(x\right)\right)=g\left(f\left(x\right)\right)=x, which of the following is true?
f(x) and g(x) are equal to each other.
f(x) and g(x) are inverse functions of each other.
f(x) and g(x) are negatives of each other.
f(x) and g(x) are reciprocals of each other.
8
The domain of f\left(x\right) is given as 3\le x\le6, while that of g\left(x\right) is 5\le x\le8.
The domain of f\left(x\right)+g\left(x\right) is 5\le x\le6.
The domain of f\left(x\right)+g\left(x\right)is 3\le x\le8
The domain of f\left(x\right)+g\left(x\right)is 3\le x\le5
The domain of f\left(x\right)+g\left(x\right)is 6\le x\le8
9
[TRIVIA] Which of the following functions has the limit definition: \lim_{n\rightarrow0}\left[\frac{x^n-1}{n}\right]
The exponential function
The natural logarithmic function
The inverse sine function
The sine function
10
\frac{d}{dx}\left(3^xe^x\right)
3^xe^x\ln\left(3e\right)
3^xe^x\ln3-e^x3^x
3^xe^x\ln\left(3^xe^x\right)
3^xe^x\left(e^x+3^x\ln3\right)
11
\lim_{z\rightarrow-\infty}\left[\frac{\sqrt{z^2-4z+3}+2z-3}{\sqrt{z^2+5z-2}-3z+5}\right]
-\frac{2}{3}
-\frac{1}{4}
1
-1
12
Given the function y=\left(x-3\right)^2+5what is the smallest value
y
can take?
-5
3
-3
5
13
The derivative
D
x
n
y
, which is the
n
th derivative of
y
with respect to
x
, is written in what notation?
Newton notation
Euler notation
Lagrange notation
Lagrange notation
14
Which of the following does not belong to the group?
1^{+\infty}
+\infty^{+\infty}
0^{+\infty}
+\infty^0
15
Evaluate the limit shown below
-\infty
+\infty
\frac{1}{3}
0
16
Which of the following is the domain of the function f\left(x\right)=\sqrt{x^2+1}?
x should be less than or equal to -1 or greater than or equal to 1.
x can be any real number.
x should be greater than or equal to 1.
x should be between -1 and 1, inclusive.
17
\lim_{\theta\rightarrow+\infty}\left[\frac{\sin\theta}{\theta}\right]
does not exist
+\infty
0
1
18
What property of logarithm should be applied to evaluate the derivative:\frac{d}{dx}\log_{x^2}\left(x+1\right)
Change-of-Base Theorem
The Logarithm of a Quotient
The Power Theorem
The Logarithm of a Product
19
\frac{d}{dx}\left(\frac{1-\cos x}{\sin x}\right)
\frac{\sin x}{\cos x}
\frac{1}{2}\sec\left(\frac{x}{2}\right)^2
-\csc x\cot x+\csc^2x
\frac{1}{2}\sec\left(\frac{x}{4}\right)^2
20
What is the 154th derivative of \sin x?
sin(x)
cos(x)
-cos(x)
-sin(x)
