Video narration
Is prashn mein x shoonya ki or ja raha hai, aur hamein diye gaye expression ka limit L nikalna hai. Aisi sthiti mein standard limit se milne wala small-x approximation istemal karenge. Jab x shoonya ke paas ho, sin(3x) lagbhag 3x hota hai, isliye sin^2(3x) lagbhag (3x)^2 hoga. Isi tarah, log(1+5x) lagbhag 5x hai. Aur exponential factor e^2x, x ke shoonya ki or jaane par, 1 ki or jata hai. Ye exact equalities nahin, balki shoonya ke paas leading behavior batate hain. Ab numerator ka leading term alag se nikalein. (3x)^2 ka maan 9x^2 hai; ise 5x se guna karne par 45x^3 milta hai. Isliye numerator lagbhag 45x^3 hai. Denominator mein x^3 maujood hai, aur e^2x ka limit 1 hai. Atah quotient mein x^3 kat jata hai, aur shesh maan 45 bachega. Isliye is limit ka maan L barabar 45 hai.