Question

Which of the following statements about hyperbolic functions is not correct ? Select one : b a csch(x) = 1/(sinh(x)); = 1 p^ 2 -p^ -1; sech(x) = 1/(mshx); = 2 e^ x +e^ -z; Atx = 0; cosh(x) = 1; x = 0 and sinh tanh(x) = (e ^ x - e ^ (- x))/(e ^ x + e ^ (- x))

Answer 1

All the given statements correctly describe the hyperbolic functions csch(x), sech(x), tanh(x), and cosh(x). The definitions for these functions are provided as csch(x) being the reciprocal of sinh(x), sech(x) the reciprocal of cosh(x), tanh(x) defined by the given formula in terms of exponential functions, and cosh(x) equalling 1 when x is 0.

Step-by-step explanation:

The question asks which statement about hyperbolic functions is not correct. The provided statements correspond to the definitions and properties of hyperbolic functions such as csch(x), sech(x), tanh(x), and cosh(x). By examining each statement:

• csch(x) = 1/sinh(x); is correct, as csch(x) is indeed the hyperbolic cosecant function which is the reciprocal of sinh(x).
• sech(x) = 1/cosh(x); is correct, as sech(x) is the hyperbolic secant function, the reciprocal of cosh(x).
• tanh(x) = (e^x - e^(-x))/(e^x + e^(-x)); is correct, since tanh(x) is the hyperbolic tangent function, defined by this formula.
• At x = 0, cosh(x) = 1; is correct, because the hyperbolic cosine function cosh(x) equals 1 when x is 0.

All the provided statements are correct with respect to the definitions and properties of hyperbolic functions. However, if the question contains typos or incorrect information not listed above, please clarify the actual statements for a proper evaluation of their accuracy.