Test 1: Limit of a Function

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Presentation transcript:

Test 1: Limit of a Function Calculate the slope of a secant to curve using the formula: 𝑚= 𝑓 𝑏 −𝑓(𝑎) 𝑏−𝑎 Calculate the slope of the tangent to curve at 𝑥=𝑎 using the formula: lim ℎ→0 𝑓 𝑎+ℎ −𝑓(𝑎) ℎ Solve real life applications involving rates of change: Average rate of change = slope of the secant. Instantaneous rate of change = slope of the tangent.

Test 1: Limit of a Function Given the graph of a function, I can: Find the value of the function at a particular spot on the domain, i.e. 𝑓 2 . Find lim 𝑥→ 𝑎 − 𝑓 𝑥 (the left sided limit) and lim 𝑥→ 𝑎 + 𝑓 𝑥 (the right sided limit) and use this to determine the existence and value of lim 𝑥→𝑎 𝑓 𝑥 . Use this information to determine continuity at a point. Given the equation of a function, I can: Find the value of the function at a particular spot on the domain, i.e. 𝑓 2 . Find lim 𝑥→ 𝑎 − 𝑓 𝑥 (the left sided limit) and lim 𝑥→ 𝑎 + 𝑓 𝑥 (the right sided limit) and use this to determine the existence and value of lim 𝑥→𝑎 𝑓 𝑥 . Use this information to determine continuity at a point.

Test 1: Limit of a Function Calculate the limit algebraically, when it exists using: Direct substitution (polynomial functions). Factoring (rational functions) – trinomials, difference of squares/cubes, grouping, etc. Rationalizing the numerator and/or the denominator using the conjugate. Substitution – i.e. let 𝑢=( 𝑥+4) 1 3 →𝑥= 𝑢 3 −4 , don’t forget to change the limiting value. Exploring the right and left sided limits of piecewise functions, including absolute value. Sketch the graph of a function given details of the function, i.e. : The value of the function at particular points. Limiting values. Details about direction and/or continuity.

Review Questions Review P.56 – 59 #1, 2ac, 3, 4, 6abd, 7, 8, 9, 11, 15c, 17, 18abc, 19a Practice Test P.60 #3, 6, 7, 8