Question

Lim y->x (y sec y - x sec x/ y-x)

Answer 1

L - Hospital is the easiest method for solving these type of questions .

Here given, $\bold{\lim_{y\to\ x}{\frac{ysecy-xsecx}{y-x}}}$
put y = x for checking form of limit .
(xsecx - xsecx)/(x - x) = 0/0 is the form of limit .

We know, we can apply L- Hospital in 0/0 and ∞/∞ forms .
so, app L- Hospital rule .
Differentiate numerator and denominator separately .
$\bold{\lim_{y\to\ x}{\frac{y(secy.tany) + secy - 0}{1 - 0}}}$
Now, put y = x
Value of limit is x(secx.tanx) + secx

Hence, answer is x(secx.tanx) + secx

Answer 2

Solution:-

given by:-

》Lim y->x (y sec y - x sec x/ y-x)

》(0/0 form)

》applied L' HOSPITAL RULE

》Lim y->x ( d/dy(ysecy) -d/dy(xsec)/(d/dy(y-x)

》= Lim y->x [(yd/dx(secy)+(secy)d/dx(y)-0)]/1-0

》= Lim y->x[ ysecy.tany +secy.1]/1

》= Lim y->x (ysecy.tany+secy)

》= [ x(secx.tanx )+secx] ans

☆i hope is help☆