Answer to Question #177367 in Trigonometry for Yusuf Idris

Question #177367

Evaluate: Lim x ²cos3x ÷ x³ + 4x²

x tend to 0


1
Expert's answer
2021-04-14T14:36:08-0400

"\\text{lim}\\frac{x^2cos3x}{x^3}+4x^2 \\text{ as x tends to 0}"

"=\\text{lim}\\frac{cos3x}{x}+4x^2"

"=\\text{lim}\\frac{cos3x}{x}+lim4x^2"

"\\text{Using l'hopital rule we find limit for } \\text{lim}\\frac{cos3x}{x}"

"=lim(-3sinx)\\text{ as x tends to 0 }"

"=0"

"lim4x^2=0" as x tends to 0

"Hence \\text{ lim}\\frac{x^2cos3x}{x^3}+4x^2 =0"


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