Apentix/AP Calculus AB/Unit 1: Limits and Continuity/Question
AP Calculus ABmediummcq1 pt

lim⁡h→014+h−14h=\lim_{h\to 0}\dfrac{\frac{1}{4+h}-\frac{1}{4}}{h}=

A.116\frac{1}{16}
B.00
C.−116-\frac{1}{16}
D.−14-\frac{1}{4}

Explanation

Core Concept

Combine the fractions: 14+h−14=4−(4+h)4(4+h)=−h4(4+h)\frac{1}{4+h}-\frac{1}{4}=\frac{4-(4+h)}{4(4+h)}=\frac{-h}{4(4+h)}. Dividing by hh gives −14(4+h)-\frac{1}{4(4+h)}, which approaches −116-\frac{1}{16}.

Correct Answer

C−116-\frac{1}{16}

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