Question

19. lim a secarx->0

Answer 1

Let the function be,

f( x )=xsecx

We have to find the value of the given function at limit x→0 .

From the trigonometric identity, the inverse of secx is cosx Now the function becomes,

f( x )=xsecx = x cosx

So we need to check the function by substituting the value at particular point (0), so that it should not be of the form 0 0 .

If the condition is true, then we need to simplify the term to remove 0 0 form.

f( x )= 0 cos0 = 0 1

Now we found that it is not in 0 0 form.

From the definition of limits, lim x→a f( x )= lim x→a p( x ) q( x ) = p( a ) q( a )

Now we can directly apply the value of limits to the given function;

lim x→0 x cosx = 0 cos0 = 0 1 =0

Thus, the value of the given expression lim x→0 xsecx=0 .