Describe how the concepts from limits, continuity of functions, an intermediate value of Theorem, and vertical asymptotes can be applied in this scenario.

This assignment is for Calculus I.
Please review the below requirements and the attached graph for scenario#.
CALCULUS I – ASSIGNMENT REQUIREMENTS:
Scenario#1 (2 Pages, 1 APA citation)
A curve
with equation y=−(x−1)^2 + 4 and
some rectangles shaded underneath. (
Suppose
we want to estimate the area under the curve y=−(x−1)^2
+ 4 on a certain interval using the rectangles provided.
Choose your own interval
based on scenario #1 above and address the following:
MUST RESPOND TO EACH POINT SEPARATELY
1. Describe
how the concepts from limits, continuity of functions, an intermediate value of Theorem, and vertical asymptotes can be applied in this scenario.
2. Estimate
the area under the curve y=−(x−1)^2+4
on the interval
from x=0 to x=3 using the rectangles provided (see attached graph).
3. Provide
another example of a scenario that involves the same concept.

Scenario#2 (2 Pages, 1 APA citation)
A
vehicle is driving along a road. Its position function is given by a function
s(t), where s is measured in feet and t is measured in seconds. Create
your own function based on scenario#2 and address the following:
MUST RESPOND TO EACH POINT SEPARATELY
1.
Draw a graph or figure to represent this situation.
2.
Describe how the concepts “Derivative of a function at a point using limits, the slope of a tangent line, piecewise function, and higher-order derivative of a function” can be applied in scenario#2.
3.
Find the instantaneous velocity of the vehicle
at seconds.
4.
Provide another example of a scenario that involves the same
concept.

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