Hyperbolic Functions and Their Properties - One Line Questions
1.
What is the value of lim (x->-infinity) tanh(x)? —
-1
2.
The integral of csch^2(x) dx is: —
-coth x + C
3.
What is the derivative of csch x with respect to x? —
-csch x coth x
4.
What is the derivative of coth x with respect to x? —
-csch^2(x)
5.
What is the derivative of sech x with respect to x? —
-sech x tanh x
6.
The inverse hyperbolic sine function, arcsinh(x), has a range equivalent to: —
(-infinity, infinity)
7.
Which of the following is a logarithmic form for arctanh(x)? —
(1/2)ln((1+x)/(1-x))
8.
Which of the following is the definition of the hyperbolic sine function (sinh x)? —
(e^x - e^-x) / 2
9.
What is the definition of the hyperbolic cosine function (cosh x)? —
(e^x + e^-x) / 2
10.
The range of the hyperbolic sine function (sinh x) is: —
(-infinity, infinity)
11.
The range of the hyperbolic cosine function (cosh x) is: —
[1, infinity)
12.
The range of the hyperbolic tangent function (tanh x) is: —
(-1, 1)
13.
The inverse hyperbolic cosine function, arccosh(x), has a domain equivalent to: —
[1, infinity)
14.
The identity cosh^2(x) - sinh^2(x) is equivalent to which value? —
1
15.
What is the value of sinh(0)? —
0
16.
What is the value of cosh(0)? —
1
17.
What is the value of lim (x->infinity) tanh(x)? —
1
18.
What is the value of lim (x->infinity) coth(x)? —
1
19.
The derivative of arctanh(x) with respect to x (for |x| < 1) is: —
1 / (1 - x^2)
20.
The derivative of arccosh(x) with respect to x (for x > 1) is: —
1 / sqrt(x^2 - 1)
21.
The derivative of arcsinh(x) with respect to x is: —
1 / sqrt(x^2 + 1)
22.
What is the value of sinh(ln(3))? —
4/3
23.
What is the value of cosh(ln(2))? —
5/2
24.
The hyperbolic functions are closely related to which geometric shape? —
Hyperbola
25.
Hyperbolic functions are sometimes called 'circular functions' because of their relationship to the equation of a: —
Hyperbola
26.
The derivative of sinh x with respect to x is: —
cosh x
27.
The expression e^-x can be represented in terms of hyperbolic functions as: —
cosh x - sinh x
28.
Which of the following is the definition of the hyperbolic cotangent function (coth x)? —
cosh x / sinh x
29.
The integral of sinh x dx is: —
cosh x + C
30.
The expression cosh(x+y) expands to: —
cosh x cosh y + sinh x sinh y
31.
Which of the following is NOT an identity for hyperbolic functions? —
1 - tanh^2(x) = sech^2(x)
32.
Which hyperbolic identity is analogous to sin^2(x) + cos^2(x) = 1? —
cosh^2(x) - sinh^2(x) = 1
33.
Which hyperbolic identity is analogous to cos(2x) = cos^2(x) - sin^2(x)? —
cosh(2x) = 2cosh^2(x) - 1
34.
What is the value of lim (x->0+) coth(x)? —
infinity
35.
The integral of tanh x dx is: —
ln(cosh x) + C
36.
What is the integral of coth x dx? —
ln(sinh x) + C
37.
Which of the following is a logarithmic form for arccosh(x)? —
ln(x + sqrt(x^2 - 1))
38.
Which of the following is a logarithmic form for arcsinh(x)? —
ln(x + sqrt(x^2 + 1))
39.
Which hyperbolic function is defined as 1/sinh x? —
csch x
40.
Which hyperbolic function is defined as 1/cosh x? —
sech x
41.
The derivative of tanh x with respect to x is: —
sech^2(x)
42.
Which hyperbolic function is analogous to the tangent function in trigonometry? —
tanh x
43.
What is the derivative of cosh x with respect to x? —
sinh x
44.
What is the definition of the hyperbolic tangent function (tanh x)? —
sinh x / cosh x
45.
What is the integral of cosh x dx? —
sinh x + C
46.
The expression e^x can be represented in terms of hyperbolic functions as: —
sinh x + cosh x
47.
The expression sinh(x+y) expands to: —
sinh x cosh y + cosh x sinh y
48.
Which hyperbolic identity is analogous to sin(2x) = 2sin(x)cos(x)? —
sinh(2x) = 2sinh(x)cosh(x)
49.
The integral of sech^2(x) dx is: —
tanh x + C