Math 21C Homework

Classical Homework Assignments

These problems are NOT required for submission. Even though these problems are optional, you are responsible for knowing how to solve all of them and are highly encouraged to try as many as possible.

Solutions are provided by Dr. Kouba.

HW#1: Section 10.1 (pg 559): # 2, 3, 4, 8, 11, 12, 13, 16, 20, 26 (Hint: Use least integer function.), 28 (Use Sandwich Theorem.), 32, 33, 35, 39 (Use Sandwich Theorem.), 40, 42, 43, 46 (Use Sandwich Theorem.), 48, 49, 52, 54, 60, 63 (Use Sandwich Theorem.), 74, 78, 81, 87, 99, 108 (Assume the case where x>1.) ... Worksheet 1 ... Solutions

HW#2: Section 10.2 (pg 569): # 7, 8, 12, 14, 42, 45, 50, 51, 52, 54, 60, 62, 63, 67, 20, 21, 86, 90, 93 ... Solutions

HW#3: Section 10.3 (pg 575): # 13, 15, 16, 17, 19, 22, 24, 26, 30, 32, 33, 35, 38, 43, 58 ... and ... Problems Using Star and Double Star From Class ... Solutions

HW#4: Section 10.4 (pg 580): # 18, 19, 22, 26, 27, 28, 30, 31, 33, 34, 36, 37, 45, 47, 52, 54, 56, 58 ... Solutions

HW#5: Section 10.5 (pg 585): (Use Ratio or Root Test) # 17, 20, 29, 34, 35, 37, 38, 46, 47, 55, 58 ... and ... (pg 585): (Use any test) # 22, 23, 24, 26, 27, 29, 31, 39 ... Solutions

HW#6: Section 10.6 (pg 591): # 1, 9, 10, 11, 13, 14, 16, 17, 19, 20, 22, 25, 27, 28, 31, 33, 36, 40, 41, 50, 58, 62, 66 ... Solutions

HW#7: Section 10.7 (pg 600): # 1, 4, 6, 7, 10, 12, 17, 24, 25, 27, 29, 44, 46, 56 ... Solutions

HW#8: Section 10.8 (pg 606): # 3, 6, 7 (with f(x) = cos x), 10 (with f(x) = sqrt(x+4)), 11 (Use the Maclaurin series for e^x.), 13 (Use the Maclaurin series for 1/(1-x).), 15 (Use Maclaurin series for sin x.), 25, 27, 29, 41, 43 ... Solutions

HW#9: Section 10.9 (pg 613): # 1, 12, 16, 17 (Do 2 ways : i. trig identity 1st, ii. series multiplication), 19, 20, 21 (Do 2 ways: i. differentiation, ii. multiplication of series), 22, 37, 40 (Begin by finding the first 4 nonzero terms and the general formula for the Maclaurin Series for f(x)= sqrt(1+x).), 41, 48 ... Solutions

HW#10: Section 10.10 (pg 620): # 2, 7, 15, 17, 20, 25, 28, (For 29, 32, and 34 also use L'Hopital's Rule to evaluate limits.), 59, 62 ... Solutions

HW#11: Section 12.1 (pg 836): # 1, 3, 6, 8, 12, 17, 18, 20ac, 17b, 22, 26-28, 30-32, 34, 36-39, 42, 43, 47, 52, 55, 58, 59, 60 ... Solutions

HW#12: Section 12.2 (pg 690): # 1, 4, 6, 7, 9-13, 16, 18, 21, 23, 25, 28, 29, 31, 33, 35, 38, 40, 41 ... Solutions

HW#13: Section 12.3 (pg 698): # 1, 4, 7, 10, 12, 13, 16, 17 (See properties of Dot Product on page 695.), 22-25, 27, 43, 49 ... Solutions

HW#14: Section 12.4 (pg 376): # 2, 3, 7, 9, 10, 14, 16 (Let P=(2,-2,1)), 19, 20, 23, (See definition of torque on page 703.) 25, 27-29, 31, 33, 36, 40 ... Solutions

HW#15: Section 12.5 (pg 712): 1, 4, 6-8, 10, 21, 22, 24, 25, 28, 31, 34, 43, 45, 47, 55, 59, 67 ... Solutions

HW#16: Section 12.6 (pg 718): # (Sketch in 2 dimensions, then 3 dimensions) 13 (Repeat the process of #13 for the equations: Ex 1) x^2 + z^2 = 4 and 2) x = y^2), (For next 5 problems use intercepts, traces, and the indicated values of z's for level curves to create a topographical map for the surface.) 18 (Use z=-4, -2, 0, 2, 4), 22 (Use z=8, 7, 4, -1, -8), 25 (Use z=-2, -1, 0, 1, 2), 27 (Use z= -sqrt{8}, -sqrt{3}, 0, sqrt{3}, sqrt{8}) ...... and ..... Section 14.1 (pg 771): # (Determine and sketch domain) 18ab, 19ab, 23ab, 24ab, 25ab ... Solutions

HW#17: Section 14.2 (pg 779): # 1, 4, 9, 12, 14, 16, 20, 41-44, 47 ... and ... (pg 847): 12, 16... Solutions

HW#18: Section 14.3 (pg 790): # 2, 7, 10, 13, 16, 21,43, 45, 46, 54, 65, 75, 76, 81, 84 ... Solutions

HW#19: Section 14.4 (pg 800): # 1 (Change the function to w=x^2+2y.), 6, 8, 9, 14, 15, 20, 22, 24, 26, 28, 42, 43, 44a ... and ... 2nd order Chain Rule Problems ... Solutions

HW#20: Section 14.5 (pg 808): # 2, 7, 10, 12, 15, 16, 19, 22, 31, 35, 36a ... Solutions

HW#21: Section 14.6 (pg 817): # 1, 4, 9, 12, 14, 15, 20, 21 ... Solutions

HW#22: Section 14.7 (pg 826): # 1, 3, 15, 16, 19, 22 ... Solutions

HW#23: Section 14.7 (pg 826): # 31 (REWRITE PROBLEM: Use the triangle formed by the graphs of x=0, y=3, and y=x.), 34, 41 (For the remaining two problems you need only find the critical points and extreme values. You need NOT verify that each corresponds to a maximum or minimum.) ... and ...
I.) The material for the top and bottom of a rectangular box costs 3 cents per square foot, and that for the sides costs 2 cents per square foot. What are the cost and dimensions of the least expensive box that has a volume of 1 cubic foot ?
II.) Determine the dimensions and volume of the closed rectangular box of largest volume if the total surface area is to be 12 square meters. ... Solutions

HW#24: Section 14.8 (pg 836): # 1, 3, (Minimize distance squared.) 8, 14, (Minimize distance squared.) 21, 27, 30, 33, (Minimize distance squared.) 35 ... Solutions

Written Homework Assignments

Read, Reflect, and React Prompt #1

Read, Reflect, and React Prompt #2

Read, Reflect, and React Prompt #3

Read, Reflect, and React Prompt #4