Question

answer!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

110 . lim ( n→ ∞) { 1.3.5...…(2n-1)}(n+1)⁴/n⁴{1.3.5......(2n -1)( n +4)}

lim( n→ ∞) {( n +1)⁴/n⁴( n +1) }

lim ( n→ ∞) { ( n+1/n)⁴ × 1/( n+1)}

lim( n → ∞) { (1 + 1/n )⁴ × 1/( n+1)}
put n = ∞

= (1 + 0) × 0 = 0






111.
lim( x→ ∞) [ √(x² +a²) - √(x²+ b² ) ]/[ √(x²+c²) -√( x² + d2) ]

this limit in the form of ∞/∞

now rationalise numerater or denominator .

lim( x→∞) {x² + a² - x² -b²}/{√(x² + a²)+√(x² + b²) } × { x² + c² -x² -d² }/{√(x²+c²) + √(x² + d²) }

lim( x→ ∞) ( a² -b²)/(c²-d²) [x{√(1+a²/x²)+√(1+b²/x²)}/x{√(1+c²/x²) + √(1+d²/x²)}

= ( a²-b²)(2)/(c²-d²)(2)

=(a²-b²)/(c²-d²)