Frazier Ward
05/11/2023 · Junior High School
QUESTION 1 (a) Calculate the limits of the following functions (if there exist): (i) (ii) \( \lim _{x \rightarrow 0} \frac{x^{2}-5 x+6}{2 x+8} \) (iii) (iv) (v) \( \lim _{x \rightarrow-\infty} \frac{\sqrt{2 x+3}-\sqrt{3 x+3}}{\sqrt{x+4}-\sqrt{2 x+4}} \) (vi) (vii) \( \lim _{x \rightarrow-\infty} \frac{1+\sin 3}{\cos x} \) \( \lim _{x \rightarrow 0} \frac{\sin (4 x) \cos (2 x)}{\tan (5 x)} \) (3)
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The limits are: \( \lim _{x \rightarrow 0} \frac{x^{2}-5x+6}{2x+8} = \frac{3}{4} \), \( \lim _{x \rightarrow-\infty} \frac{\sqrt{2x+3}-\sqrt{3x+3}}{\sqrt{x+4}-\sqrt{2x+4}} \) is undefined, \( \lim _{x \rightarrow-\infty} \frac{1+\sin 3}{\cos x} \) cannot be calculated directly, and \( \lim _{x \rightarrow 0} \frac{\sin (4x) \cos (2x)}{\tan (5x)} = \frac{4}{5} \).
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