f(x) = sec x
f'(x) = sec x • tan x
The function f(x) = sec x is an even function which means it has reflective symmetry about the y-axis. It is an inverse trigonometric function of cosine.
The domain of the function f(x) = sec x is all real numbers except for x = (2n + 1)π/2, where n is any integer. At these points, the function approaches infinity or negative infinity.
The range of the function f(x) = sec x is the set of all real numbers except for values between -1 and 1. This is because the function is undefined for these values since the secant of an angle is 1 divided by the cosine of that angle, and cosine is never greater than 1 or less than -1.
The period of the function f(x) = sec x is 2π. This is because the secant function has a period of 2π just like the cosine and sine functions.
The function f(x) = sec x has vertical asymptotes at x = nπ + π/2, where n is any integer. The function approaches infinity or negative infinity as it approaches these points from either side of the x-axis.
The function is continuous everywhere except at the vertical asymptotes where it is undefined.
The derivative of f(x) = sec x is f'(x) = sec x tan x. This can be derived using the quotient rule and the fundamental identity of trigonometry.
The integral of f(x) = sec x is given by ∫sec x dx = ln|sec x + tan x| + C, where C is the constant of integration.
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