Evaluate the Limit limit as x approaches 0 of sec(2x)

Problem

(lim_x→0)(sec(2*x))

Solution

1. Identify the type of limit and the function involved. The function is sec(2*x) which is the reciprocal of cos(2*x)

2. Check for continuity at the point x=0 The function cos(2*x) is continuous everywhere, and cos(2*(0))=cos(0)=1 Since the denominator is not zero, the function sec(2*x) is continuous at x=0

3. Apply direct substitution by plugging x=0 into the expression.

4. Evaluate the trigonometric value. Since cos(0)=1 then sec(0)=1/1=1

Final Answer

(lim_x→0)(sec(2*x))=1

Want more problems? Check here!