What is the limit as x approaches pi/2 of 7sec(x)-7tan(x) ?

The limit as x approaches pi/2 of 7sec(x)-7tan(x) is 0

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limit as x approaches pi/2 of 7sec(x)-7tan(x)

x \to \frac{π}{2} lim (7 sec (x) - 7 tan (x))

0

Solution steps

x \to \frac{π}{2} lim (7 sec (x) - 7 tan (x))

Multiply by the conjugate of

7 sec (x) - 7 tan (x) : \frac{49}{7 sec ( x ) + 7 tan ( x )}

= x \to \frac{π}{2} lim (\frac{49}{7 sec ( x ) + 7 tan ( x )})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 49 \cdot x \to \frac{π}{2} lim (\frac{1}{7 sec ( x ) + 7 tan ( x )})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= 49 \cdot \frac{lim _{x \to \frac{π}{2}} ( 1 )}{lim _{x \to \frac{π}{2}} ( 7 sec ( x ) + 7 tan ( x ) )}

x \to \frac{π}{2} lim (1) = 1

x \to \frac{π}{2} lim (7 sec (x) + 7 tan (x)) = - \infty

= 49 \cdot \frac{1}{- \infty}

Simplify

49 \cdot \frac{1}{- \infty} : 0

= 0

What is the limit as x approaches pi/2 of 7sec(x)-7tan(x) ?
The limit as x approaches pi/2 of 7sec(x)-7tan(x) is 0