MAC2311TEST2SolutionsSpring2011

MAC2311TEST2SolutionsSpring2011 - MAC 2311 CALCULUS WITH...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MAC 2311 CALCULUS WITH ANALYTIC GEOMETRY ONE TEST 2 Ou’i’ of Name S Score 50 Directions: Answer each question, showing ALL your work for full credit. 1. Calculate the derivative of each of the following functions. (8 points) f (x) = 7: 2x + é—x6 — «5 (Reduce any fractions in the final answer) g(x) = —x’4 + 5 V; (Express answer in radical notation with no negative exponents) h(x) = x2 sinx + 2x cosx — 25inx (Simplify completely by combining like terms) b] (X): 33X MAX +XD‘COSX +RcorX-stsnx- Q Cosx k(x) = sec(x2) Valencia Community College 2. Let f and g be functions whose graphs are shown below. Suppose that P(x) = f (x) - g(x) and C (x) = f (g(x)). Calculate, step by step, the values of P’(2) and C '(2). (6 points) Valencia Community College Find the equation of the tangent line to the graph of y = \/ tanx at x = E. U 4 se EXACT answers involving “pi” in your final response. (5 points) ‘ {5% 3:: L. Secax L/ flag. in x: 1 3 ~ 3 $5th RY get :: {a 2 z 3}— Valencia Community College . A particle moves along a straight line whose position at any time is given by the equation 1 . . . s = 1— 5 t + 3t2 — 313 where t Z 0 , 2‘ IS measured 1n seconds and 5 1n feet. Answer the following questions. Be careful of signs. a) When is the particle moving in the negative direction? (2 points) M4540 my“ .. ' “r5 v: awe-6:0 b) c) What is the total displacement of the particle during the first 6 seconds of travel? (1 point) 5305"“503‘): $~l =§6~tté d) What is the total distance traveled by the particle during the first 6 seconds? (2 points) Valencia Community College Sm (X-HA == weasg M’m (“Ema ffié r K, 1 0‘3 Cos(x+ g)[i+ 3%} = (B £039, + XE 8m?) .332 clfivwe \ (’8 ()(+3\ 1-. C933 —'7(S‘m5~ d9 Cos (x+e.)—\- chs j; 7(3ij ~ 0‘9 + $3- QosQQi-g) = C053 “503(X’f3) 33: cm @W a; ’ xsing + COSDH’SB Valencia Community Coilege 6. For What values of x on the interval [0,47r] does the graph of f (x) = Xx/E — 2cosx have a horizontal tangent? Note: you are going around the unit circle twice. Use EXACT answers involving “pi” in your final response. (6 points) $00: $5 +Qs‘m'xzo 9w”: 4:; saw is maeler ‘m "toadmwlsilll: cmlm “a , Valencia Community College x k 7. The derivative of f (x) = can be written in the form f ’(x) = where k and m \j x 2 + 4 (x2 + 4)“ are real numbers. Find the exact values for k and m . (6 points) 43 ' (X\= (M Xq-H-l — (543% Q R 4an _ X‘+Ll—->< : ‘l " 3/ 3/ XR+L\ (XOR-Ll} Q (xiii—if 9‘ Valencia Community College 8. The surface area of a sphere is increasing at a rate of 3768 cm2 per second. Find the rate at which volume of the sphere is increasing when the equator of the sphere is 314 cm ? (6 points) The volume of a sphere in terms of its radius is V = g7: r3 The surface area of a sphere in terms of its radius is A = 47: r2 Note: For simplicity, use the number 3.14 as an approximation for “pi” in ALL of your calculations. Be sure to include the units of measurement in your final answer. ;\ om“ [KW V393” W3 A: Ll’irra WW6” r z .331. on OW _ a3 fin: 8’“th 3‘“ ‘E ~ Ll'h’l‘ ii. are '(E dA wrfifig on air 3%? o“ ‘8 —-—--~: dz: WM} dk gfifr ow : ex _ ,5; l Ll r‘ clv _ law 231:) ‘afg — 3"“ é‘i: cmdoo m3 bk :6: ------------------------- --End of Test----------——--—-------------—— Valencia Community College ...
View Full Document

This note was uploaded on 10/18/2011 for the course MAC 2311 taught by Professor Jameslang during the Fall '11 term at Valencia.

Page1 / 8

MAC2311TEST2SolutionsSpring2011 - MAC 2311 CALCULUS WITH...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online