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# 241mid1 - I Calculus I(Math 241 —— Test 1 Problem 1[10...

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Unformatted text preview: I Calculus I (Math 241) —— Test 1 Problem 1. [10 Points] Use ﬁrst-principles (the deﬁnition of the derivative and the computation of the limit of the appropriate difference quotient) to ﬁnd the derivative of the function f (as) = 1/ 53 at a: = 3. Problem 2. [10 Points] Find the equation of the tangent line to the graph of the function f(:c) = tang: at the point (x, y) = (“FT/6,1/x/g) Problem 3. [10 Points] Suppose you are told that (1) lim f(m) = 1. :I:—>5 1. Which assumption is made about the domain of the function ﬁx)? 2. What is the precise mathematical meaning of (1)? Le, spell out the definition of a limit with the given data. Problem 4. [10 Points] Below you see the graph of the function h(\$) De— cide for each of the points x = . 1, 2, 3, and 4, Whether the function has a limit at the point, whether the function is continuous at the point, and whether the function has a left or right sided limit at the point. If there is a limit, or one sided limit, then tell what it is. Problem 5. [10 Points] Consider the curve given by the equation y2 = 3:3(2 — :c). Find its slope dy/da: at the point (1,1) on the curve, as well as the equation for the tangent line at this point. Problem 6. [10 Points] A kite 100 ft above the ground moves horizontally at a speed of 8 ft / sec. At what rate is the angle between the string and the horizontal decreasing when 200 ft of string have been let out? Problem 7. [10 Points] Use approximation by differentials to find an ap- proximate value for the 5-th root of 250. Hint: Use that 35 = 243. 1’ \ M ") TM \$“m—J‘io“ Wm}? (0e Gaigxmd W 0va :MIFCTVQJ. ‘ kWal‘b‘k'ekLnaﬁA—{f 5515:235‘“ ) Emﬂec‘l‘q ”I J km god-13, m0 DJLME'\' CL"! \) MT)" COKEVIKDMQ+ I, x—‘n 1—91" L‘wx 9‘06 = 2‘ ﬂu“ QM=OO , ‘AO LN; a} 0?: ,hosr mnknuouAaJI-L ‘ + Y “’73 X—vz QXM QC!) : Q‘.Mx QR): QDMetsc) = 2. = 9(3)); OOWRHMOM Q4» 3. x-ea? xa5+ gab; Q3“ QM -‘= QM QM = ,QCM Rm = i. ")AUHL'RS x—aH: . )<--=>L+'r ‘i-“i- ) Mo’r Gem-knuom o-‘r ‘4. .1... __ IZZJ. 535-0 1- §(:50\~ 3+ Lt‘OS L'l'ﬁs #kk‘ihook Sufﬁx-k0“ \$5.1 r-Pm‘olewk GD : EH3: Haﬁz) MO?" . , = (8—0 ; MR Unﬁt); oi, ”M41341. LshLQ At“ 0‘ V/XZﬁ]+'°'OL Wv’edhi '36 “’2. :2 W0 (X’TO-‘rmﬂ - Gk -9; x '_' L 2‘ 4! ;K(t)' C0304 (iii-Lg: 493(x (HA-um] TE Date: m I Calculus I- Name: Score: — Derivative Gateway Test ID #: Pass? ‘ _ Section: Find the derivative of each of these= but DO NOT SIMPLIFY. Calculators are not allowed. Pasaing is 5 out of 6. Passed exams will be given to your instl‘uctor‘ Allowed time: 15 minutes. 1.-3,r=(3:)4-2 1?. a” H X V3 —-?> 2 h(t)=x/_et+1)3 (54L) _ 30:14)- a' 2 g so”: .5 +_ c; “My” LG I_ (.6 X‘6 {23:44) —— Y .‘2 :3 Qx-le 4.1 =(2m—1)3-:t+3:r5 C"! 3‘: Mac—\$2 _ . + 3H 5- ﬁx} = csc (cos(2:c} + 2) ﬁr: ._ Cgc (th'l‘lh (Ml (On “xii.“ (" :2 SN (2%)) agm=ssma¢é am21§e¢&)fj“(l3fsw-s\ do 9 1: (T35 ﬁ\$ (aftlléecf Sal - Aeds?‘ Hang a /' * q(2r\$ ~- I} +‘éaﬂél' - Wb(YZ\$ 33 2 5 3HT) ...
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241mid1 - I Calculus I(Math 241 —— Test 1 Problem 1[10...

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