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The Concept of a Limit- HW problems
1. An object is launched vertically upwards at 64 ft/sec. The height in
feet of the object above the ground is given by 𝑠(𝑡) = −16𝑡 2 + 64𝑡,
0 ≤ 𝑡 ≤ 4, where 𝑡 is in seconds. Find the average velocity over the
following intervals:
a. 2 ≤ 𝑡 ≤ 4
𝑏. 2 ≤ 𝑡 ≤ 3
𝑐. 2 ≤ 𝑡 ≤ 2.1
𝑑. 2 ≤ 𝑡 ≤ 2.01
𝑒. 2 ≤ 𝑡 ≤ 2 + ℎ, where ℎ > 0
What is the instantaneous velocity at 𝑡 = 2.
2. Suppose 𝑓 (𝑥 ) = 𝑥 2 − 4𝑥 + 2. Find the slope of the secant line
between the point where 𝑥 = 1 and
𝑎. 𝑥 = 3
𝑏. 𝑥 = 2
𝑐. 𝑥 = 1 − ℎ, ℎ > 0
What is the slope of the tangent line to 𝑦 = 𝑓(𝑥) at 𝑥 = 1.
3. Suppose 𝑓 (𝑥 ) = 𝑥 3 + 𝑥. Find the slope of the secant line between
𝑥 = 1 and 𝑥 = 1 + ℎ, ℎ > 0. What is the slope of the tangent line to
𝑦 = 𝑓(𝑥) at 𝑥 = 1.
The Concept of a Limit- HW problems
1. An object is launched vertically upwards at 64 ft/sec. The height in
feet of the object above the ground is given by 𝑠(𝑡) = −16𝑡 2 + 64𝑡,
0 ≤ 𝑡 ≤ 4, where 𝑡 is in seconds. Find the average velocity over the
following intervals:
a. 2 ≤ 𝑡 ≤ 4
𝑏. 2 ≤ 𝑡 ≤ 3
𝑐. 2 ≤ 𝑡 ≤ 2.1
𝑑. 2 ≤ 𝑡 ≤ 2.01
𝑒. 2 ≤ 𝑡 ≤ 2 + ℎ, where ℎ > 0
What is the instantaneous velocity at 𝑡 = 2.
2. Suppose 𝑓 (𝑥 ) = 𝑥 2 − 4𝑥 + 2. Find the slope of the secant line
between the point where 𝑥 = 1 and
𝑎. 𝑥 = 3
𝑏. 𝑥 = 2
𝑐. 𝑥 = 1 − ℎ, ℎ > 0
What is the slope of the tangent line to 𝑦 = 𝑓(𝑥) at 𝑥 = 1.
3. Suppose 𝑓 (𝑥 ) = 𝑥 3 + 𝑥. Find the slope of the secant line between
𝑥 = 1 and 𝑥 = 1 + ℎ, ℎ > 0. What is the slope of the tangent line to
𝑦 = 𝑓(𝑥) at 𝑥 = 1.
