Underlying Concepts of Calculus Unit Assignment You may choose to complete your mathematical calculations by hand and scan or take images to upload to the dropbox. To help your teacher review your work, please try to submit your calculations as a single le document {preferably as a pdf}. If you aren't sure how to do this, please contact your teacher for assistance. Important When answering questions in a mathematics course always be sure to use the following guidelines to help you do your best: 0 Provide full solutions, showing all of your steps. 0 Make sure that there is one step or idea per line. 0 Use one equal sign per line. 0 Make sure that equal signs line up vertically. 0 Don't use self-developed short form notations. 1. Determine the following limits {if they exist}. [2 marks each) a. Hat (33:4 + 2.1-2 5) mi3 n lim 4* 2 - +12l} 1:. 11m (1 ) :cbat S'h 2. Evaluate the following limits {if they exist}. [3 marks each} a- li": (22311) s E}. (_~m4) :cHJ c. lim (:3) 3:464 3. From first principles {i.e. using the tangent slope method], nd the slope of the following curves at the given value of at. [3 marks each] a. f(at) : 2:122 :.t:at:r.' : 3 b. y: 33:3l late: = 4 4. Look at the graph below of the derivative f! (3:). From this, make a sketch of the original function f (at) and of the second derivative f\" [:c), and explain your reasoning. [7 marks] .I