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Exercitii și probleme Reproduceți desenul. Construiţi simetricele punctelor A,B,C,D față de punctul O.

Exercitii și probleme \newlineReproduceți desenul. Construiţi simetricele punctelor A,B,C,D A, B, C, D față de punctul O O .

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Q. Exercitii și probleme \newlineReproduceți desenul. Construiţi simetricele punctelor A,B,C,D A, B, C, D față de punctul O O .
  1. Simplify expression: Simplify the expression inside the limit. 1x+4−14\frac{1}{x+4}-\frac{1}{4} over xx = 1x+4−14x\frac{\frac{1}{x+4} - \frac{1}{4}}{x}
  2. Find common denominator: Find a common denominator for the terms in the numerator.\newline(1x+4−14)=4−(x+4)4(x+4)=−x4(x+4)(\frac{1}{x+4} - \frac{1}{4}) = \frac{4 - (x+4)}{4(x+4)} = \frac{-x}{4(x+4)}
  3. Substitute simplified numerator: Substitute the simplified numerator back into the original limit expression.\newline1x+4−14\frac{1}{x+4}-\frac{1}{4}/xx = −x4(x+4)\frac{-x}{4(x+4)}/xx = −14(x+4)-\frac{1}{4(x+4)}
  4. Evaluate limit: Evaluate the limit as xx approaches 00.lim⁡x→0(−14(x+4))=−14(0+4)=−116\lim_{x \to 0} \left(\frac{-1}{4(x+4)}\right) = \frac{-1}{4(0+4)} = -\frac{1}{16}

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