Question

plzz answer limit class 12th WITHOUT L HOSPITAL RULE​

Answer 1

Solution:-

Let x-2=h

in this case clearly we can analyse that,

x=2+h

now putting the value of x

we get

=>{(4-(2+h)^2) (cosπ(2+h)/4)}/(sin(2+h-2)

=>{(4-4-h^2-4h)^1/2 ×(cosπ(2+h)/4)}/(sin(h))

=>{-h(h-4)^1/2 ×cosπ(2+h)/4}/(sin(h))

dividing denominator and numerator by h we get

=>{(4-h)^1/2 ×cosπ(2+h)/4}/sin(h)/h

we know

(sinx)/x=1

so,sin(h)/(h)=1

=>{(4-h)^1/2 ×cosπ(2+h)/4}/1

as h is trending to 0

so, neglecting h we get

=>2×cosπ/2

=>2×0=0