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Complete the missing value in the solution to the equation.

Complete the missing value in the solution to the equation.

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Find limits of polynomials and rational functionsright chevron icon

Full solution

Q. Complete the missing value in the solution to the equation.
  1. Simplify expression inside limit: Simplify the expression inside the limit.\newlinelim⁡x→0(1x+4−14)/x\lim_{x \to 0}\left(\frac{1}{x+4}-\frac{1}{4}\right)/x\newline= lim⁡x→0(4−(x+4)(x+4)⋅4)/x\lim_{x \to 0}\left(\frac{4 - (x + 4)}{(x + 4) \cdot 4}\right)/x\newline= lim⁡x→0(−x(x+4)⋅4)/x\lim_{x \to 0}\left(\frac{-x}{(x + 4) \cdot 4}\right)/x
  2. Simplify complex fraction: Simplify the complex fraction.\newline=lim⁡x→0(−x(x+4)⋅4⋅x)= \lim_{x \to 0}\left(\frac{-x}{(x + 4) \cdot 4 \cdot x}\right)\newline=lim⁡x→0(−1(x+4)⋅4)= \lim_{x \to 0}\left(\frac{-1}{(x + 4) \cdot 4}\right)
  3. Evaluate limit as xx approaches 00: Evaluate the limit as xx approaches 00.=−1(0+4)⋅4= \frac{-1}{(0 + 4) \cdot 4}=−116= \frac{-1}{16}

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