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A series of calculus problems focusing on limits, continuity, and derivatives. It includes exercises on evaluating limits from graphs, identifying points of discontinuity and non-differentiability, and applying derivative rules. The problems cover topics such as finding derivatives of trigonometric functions, exponential functions, and composite functions. Additionally, it explores tangent lines and graphical analysis of functions based on their properties. This resource is designed to enhance understanding and proficiency in calculus concepts through practical application and problem-solving.
Typology: Exams
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(@ Jim f() = O () lim^ o)^ IS0^ L
(© f(-3)= DNE (@ lim £G) = 3 (e) lim £ (x) =0ONE ™
Of= (&) lim f(x) = 2 (h) f(2) = DNE (i) At which x values is f(x) discontinous? |, 1
Problem 2: | -F'()()—.\lm n-> ey = oy _.——-—--":'"""‘ a.^ Exactly^ ONE^ of^ these^ limits^ represents^ the^ derivative^ of^ a^ function.^ Circle^ that^ ONE^ limit. (3x2—5x+7+h)—(3x*—5x+7) i 'l'i_gg h
il. Llixtl) h m(3(x+h)2—5(x+h)+7)—(3x2—Sx+7)
iv. li i B^ +h)2—5(x+h)+7)+@x2—5x+7)
b. For^ ONLY^ the^ limit^ that^ you^ circled^ in^ part^ (a),^ the^ limit^ represents^ the^ derivative^ of^ what^ function? RX): INTomy rT
Problem 3: Find the derivative of each of the following (Do not simplify your answer): a.
& t 2
VE e i s +an ()
fan Ax) Problem 4: Evaluate the following limits. Show clearly how you got your answer. a.