Limit Question

Question

How would I prove the: lim x->pi/2 on the equation (sec(x))/1+tan(x). Im stuck, thank you in advance.

Answer 1

Hi Mike,

 

Let's use trig identities to reformat the expression to see if we can use direct substitution of Π/2 to evaluate the limit.

 

Since sec x = 1/cos x and tan x = sin x/cos x, we can write (1/cos x) / (1 + sin x/cos x). Multiply top/bottom by cos x to eliminate the complex fraction, resulting in 1/(cos x + sin x).

 

Now the limit of that expression as x approaches  Π/2 can be evaluated by direct substitution = 1/( 0 + 1) = 1.

 

Try graphing the original function at https://www.desmos.com and you will see that ax x approaches Π/2 from either side the function gets close to 1.