Calculus maple Worksheet Assignment | Online Assignment

Solve the problem using maple. submit the maple file and another one in pdf.Calculus Maple Worksheet (Take-Home Midterm Exam)
Use the Maple Software to solve problems on this worksheet.
Convert your maple file to PDF File.
Submit your PDF file in CUNY Blackboard.
1. Use Maple to graph 𝑓(𝑥)=𝑎𝑥−𝑥2, for 𝑎=0,1,2,3,4,5. Use the domain of
−2≤𝑥≤7 and graph the above functions on the same 𝑥−𝑦 coordinate system. Explain what happens as the value of 𝑎 increases.
2. Frist, use Maple to evaluate the following limit. Second, verify your results graphically, numerically, and algebraically, if possible.
a) lim𝑥→1𝑥3−1𝑥5−𝑥
b) lim𝑥→01𝑥+1𝑥−1
c) lim𝑥→3√𝑥+1−2𝑥−3
d) lim𝑥→22𝑥2−7𝑥+6𝑥−2
e) lim𝑥→4𝑥−4√𝑥+5−3
f) lim𝑥→01√1+𝑥𝑥−1
3. Suppose 𝑦=𝑓(𝑥)=𝑥2+2𝑥+1 𝑎𝑛𝑑 𝑃=(−3,4).
a) Find the derivative of f(x) at the point P using the definition of a derivative.
b) Using the results in part a, find an equation of the tangent line to the graph of f(x) at the point.
c) Display the graph of f(x) and the tangent line of the same coordinate system.