Questions with Answers - Calculus and Analytic Geometry I | MATH 1823, Exams of Analytical Geometry and Calculus

Download Questions with Answers - Calculus and Analytic Geometry I | MATH 1823 and more Exams Analytical Geometry and Calculus in PDF only on Docsity! calc r — Fall ZOO — Mo dL Q1]...[15 points] Let f(x) be a function of « whose domain is all real numbers. Consider the following expression. f(z) — #2) 2-2 What is this expression called? Tris is cartep A DIF EEREACE GuoT eNT ‘Write down two interpretations of this expression. © Geomadveal +, ae EOD Lt is Vo slope of the (fe) Lene seq oro connecting bye points an Ho cap al ey) 5 namely, (x, Fay) and (2, fe) ()_ Anolyttcal. Tt rs the average rote of change of Foe) ust respect te x over the interval fad (ee Bxd r<x), Sf ner. fary— fa e Change we powkeud alunos (Gx) -values) K-22 <— Change Sw (ersscesgondivay) Xp valves (x-vahod Q2]. .. [20 points] For each of the two functions below, write down the domain, the range and sketch the graph of the function. f(z) = |x—-2| Bonen C088) 4 Range TP see) du ‘ x =p > » 2 g(a) = ||—2 y Domaia, = ‘es ) > x Range = (2, ©) Q5]. .. [15 points] Find the value of c which makes the following function continuous. Show the details of your reasoning. Keep in mind that the steps of your argument (how you arrived at a value for c) are more important than the actual value of c. f(a) = Qe +4 for <1 =) cat+e for e>1 fay = 20)+y =24+4h = 6. té fog \s tb be costhudws ) Shown Lin Fu) shad axist & be ogual t fajeb. yoe La pacticullor ) ir fx) x |* 7 Yel a vee CxXHC poRtion 5 The df ee) =& > lin (cxtc) =4 Xoit > cuy +c = > Cc +c.06UcSG > weoeb 7) |c = 3 <— Q6]...[10 points] Suppose that sin(#) = 3/5 and that 1/2 < 9 <7. Find the values of cos(@) and of tan(@). Show the details of your work. Basic PROPERTY TANIT CRC LE Caped INATES Cos?(©) + smnt(o) = \ a- Cox) = \— <n) cr6)= £ f\— swe) | ewhich sign do Wwe Une ? . “ GC heresy Now ty, <8 <0 > oO <0 > cx(e\ = lo sin ) ouc evamp\s, sm©® = 3. Tlacefore - ~ - Tn au 2 ods\e - VI(S) fe 5 tel uy So BENS (x)= -& _ sae) 3 ails ° Me tas) = Cpe = - Gf) —- -3 tanO = 2 +,