The instantaneous velocity is given as a limit, {{MATH_155}}. What is the form of this limit? The numerator {{MATH_156}} approaches {{MATH_157}} as {{MATH_158}} (since the displacement function {{MATH_159}} is continuous) and the denominator {{MATH_160}} also approaches {{MATH_161}}. This limit has form {{CMD_162}}, an indeterminate form. Let's use the same setting as before to work with this definition. {{CMD_163}} The height of a ball above the ground during the time interval {{MATH_164}}, with {{MATH_165}} is in seconds and {{MATH_166}} in feet, is given by {{MATH_167}} Find {{MATH_168}}, the instantaneous velocity of the ball {{MATH_169}} seconds after it is thrown. {{CMD_170}} From the previous example, we know that the average velocity of the ball on the interval {{MATH_171}}, for {{MATH_172}}, and the average velocity on the interval {{MATH_173}}, for {{MATH_174}}, are both given by {{MATH_175}} In order to find the instantaneous velocity {{MATH_176}}, we take the limit as {{MATH_177}} goes to {{MATH_178}}. {{ENV_179}} {{CMD_180}} {{CMD_181}}