Lesson H1-H2
H1-H2 Hyperbolic functions and their calculus Quiz: AQA Further Maths, Unit 2
20 questions
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Lesson H1-H2, Hyperbolic functions and their calculus: 20 multiple choice questions for the AQA Further Maths (7367), Unit 2: Compulsory content, written with Revision Ninja.
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The 20 questions
-
What is the range of cosh(x) for all real x?
- y >= 0
- -1 < y < 1
- All real numbers
- y >= 1
-
What is the range of tanh(x)?
- -1 < y < 1
- 0 < y <= 1
- All real numbers
- y >= 1
-
What is the range of sech(x)?
- -1 < y < 1
- All real numbers
- y >= 1
- 0 < y <= 1
-
Which value is excluded from the domain of cosech(x)?
- -1
- ln(2)
- 1
- 0
-
Which expression is the definition of sinh(x)?
- (e^(-x) - e^x)/2
- e^x - e^(-x)
- (e^x + e^(-x))/2
- (e^x - e^(-x))/2
-
What is the value of cosh^2(x) - sinh^2(x)?
- x
- cosh(2x)
- 0
- 1
-
What is the derivative of cosh(x) with respect to x?
- 1/cosh(x)
- cosh(x)
- sinh(x)
- -sinh(x)
-
What is the derivative of tanh(x)?
- sech(x)
- -sech^2(x)
- sech^2(x)
- cosh^2(x)
-
Which is the integral of sinh(x) with respect to x?
- -cosh(x) + C
- cosh(x) + C
- sinh(x) + C
- ln(cosh(x)) + C
-
Which is the integral of tanh(x) with respect to x?
- ln(sinh(x)) + C
- sech^2(x) + C
- ln(cosh(x)) + C
- tanh^2(x)/2 + C
-
Evaluate sinh(ln 2).
- 3/4
- 3/5
- 1/2
- 5/4
-
Evaluate tanh(ln 2).
- 4/3
- 5/4
- 3/5
- 3/4
-
What is the derivative of cosech(x) with respect to x?
- -cosech^2(x)
- -cosech(x) coth(x)
- cosech(x) coth(x)
- cosech(x)
-
What is the limit of tanh(x) as x tends to infinity?
- 0
- 1
- -1
- infinity
-
Evaluate the integral of cosh(x) from 0 to 1.
- ln(cosh(1))
- 1 + sinh(1)
- cosh(1)
- sinh(1)
-
Evaluate the integral of sinh(x) from 0 to 1.
- cosh(1) + 1
- sinh(1) - 1
- cosh(1) - 1
- 1 - cosh(1)
-
Differentiate x sinh(x) with respect to x.
- sinh(x) + x cosh(x)
- sinh(x) - x cosh(x)
- cosh(x) + x sinh(x)
- x cosh(x)
-
Differentiate sinh(3x) with respect to x.
- cosh(3x)
- 3 sinh(3x)
- -3 cosh(3x)
- 3 cosh(3x)
-
Find the integral of cosh(2x) with respect to x.
- (1/2) cosh(2x) + C
- 2 sinh(2x) + C
- (1/2) sinh(2x) + C
- sinh(2x) + C
-
Which property of tanh(x) holds for all real x?
- tanh(-x) = 1/tanh(x)
- tanh(-x) = sech(x)
- tanh(-x) = -tanh(x)
- tanh(-x) = tanh(x)
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