EBK FINITE MATH AND APPLIED CALCULUS
7th Edition
ISBN: 8220103612005
Author: Costenoble
Publisher: CENGAGE L
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 12.3, Problem 14E
In Exercises 11–16 the position s of a point (in feet) is given as a function of time t (in seconds). Find (a) its acceleration as a function of t and (b) its acceleration at the specified time. [HINT: See Example 1.]
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
If h(x)
=
-2x-8
49x2-9
what is lim h(x)?
x--00
Question
Find the following limit.
Select the correct answer below:
○ 0
○ 3
○ 6
∞
6x + 3e
lim
00+2
x 2
What is the limit as x → ∞ of t(x) =
=
√81x2
-3x+5
Chapter 12 Solutions
EBK FINITE MATH AND APPLIED CALCULUS
Ch. 12.1 - In Exercises 112, locate and classify all extrema...Ch. 12.1 - In Exercises 112, locate and classify all extrema...Ch. 12.1 - In Exercises 112, locate and classify all extrema...Ch. 12.1 - In Exercises 112, locate and classify all extrema...Ch. 12.1 - In Exercises 112, locate and classify all extrema...Ch. 12.1 - In Exercises 112, locate and classify all extrema...Ch. 12.1 - In Exercises 112, locate and classify all extrema...Ch. 12.1 - In Exercises 112, locate and classify all extrema...Ch. 12.1 - In Exercises 112, locate and classify all extrema...Ch. 12.1 - In Exercises 112, locate and classify all extrema...
Ch. 12.1 - In Exercises 112, locate and classify all extrema...Ch. 12.1 - In Exercises 112, locate and classify all extrema...Ch. 12.1 - In Exercises 13-44, find the exact location of all...Ch. 12.1 - In Exercises 13-44, find the exact location of all...Ch. 12.1 - Prob. 15ECh. 12.1 - Prob. 16ECh. 12.1 - In Exercises 13-44, find the exact location of all...Ch. 12.1 - In Exercises 13-44, find the exact location of all...Ch. 12.1 - Prob. 19ECh. 12.1 - In Exercises 13-44, find the exact location of all...Ch. 12.1 - In Exercises 13-44, find the exact location of all...Ch. 12.1 - In Exercises 13-44, find the exact location of all...Ch. 12.1 - In Exercises 13-44, find the exact location of all...Ch. 12.1 - Prob. 24ECh. 12.1 - In Exercises 13-44, find the exact location of all...Ch. 12.1 - Prob. 26ECh. 12.1 - Prob. 27ECh. 12.1 - Prob. 28ECh. 12.1 - In Exercises 13-44, find the exact location of all...Ch. 12.1 - In Exercises 13-44, find the exact location of all...Ch. 12.1 - In Exercises 13-44, find the exact location of all...Ch. 12.1 - Prob. 32ECh. 12.1 - In Exercises 13-44, find the exact location of all...Ch. 12.1 - Prob. 34ECh. 12.1 - Prob. 35ECh. 12.1 - Prob. 36ECh. 12.1 - In Exercises 13-44, find the exact location of all...Ch. 12.1 - Prob. 38ECh. 12.1 - In Exercises 13-44, find the exact location of all...Ch. 12.1 - Prob. 40ECh. 12.1 - In Exercises 13-44, find the exact location of all...Ch. 12.1 - Prob. 42ECh. 12.1 - In Exercises 13-44, find the exact location of all...Ch. 12.1 - Prob. 44ECh. 12.1 - In Exercises 4548, use graphing technology and the...Ch. 12.1 - Prob. 46ECh. 12.1 - Prob. 47ECh. 12.1 - Prob. 48ECh. 12.1 - In Exercises 4956 the graph of the derivative of a...Ch. 12.1 - Prob. 50ECh. 12.1 - In Exercises 4956 the graph of the derivative of a...Ch. 12.1 - Prob. 52ECh. 12.1 - In Exercises 4956 the graph of the derivative of a...Ch. 12.1 - Prob. 54ECh. 12.1 - Prob. 55ECh. 12.1 - Prob. 56ECh. 12.1 - Prob. 57ECh. 12.1 - Prob. 58ECh. 12.1 - Draw the graph of a function that has stationary...Ch. 12.1 - Prob. 60ECh. 12.1 - Prob. 61ECh. 12.1 - Prob. 62ECh. 12.1 - We said that if f is continuous on a closed...Ch. 12.1 - Prob. 64ECh. 12.1 - Prob. 65ECh. 12.1 - Prob. 66ECh. 12.2 - In Exercises 1-8, solve the given optimization...Ch. 12.2 - In Exercises 1-8, solve the given optimization...Ch. 12.2 - In Exercises 1-8, solve the given optimization...Ch. 12.2 - In Exercises 1-8, solve the given optimization...Ch. 12.2 - In Exercises 1-8, solve the given optimization...Ch. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - For a rectangle with perimeter 20 to have the...Ch. 12.2 - Prob. 10ECh. 12.2 - Advertising Costs The cost, in thousands of...Ch. 12.2 - Advertising Costs The cost, in billions of...Ch. 12.2 - Average Cost: iPhones Assume that it costs Apple...Ch. 12.2 - Prob. 14ECh. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Fences I would like to create a rectangular...Ch. 12.2 - Fences I would like to create a rectangular orchid...Ch. 12.2 - Prob. 21ECh. 12.2 - Prob. 22ECh. 12.2 - Fences (Compare Exercise 19.) For tax reasons I...Ch. 12.2 - Fences (Compare Exercise 20.) For reasons too...Ch. 12.2 - Revenue Hercules Films is deciding on the price of...Ch. 12.2 - Prob. 26ECh. 12.2 - Prob. 27ECh. 12.2 - Projected Revenue: Smartphones Worldwide annual...Ch. 12.2 - Revenue: Monorail Service The demand for monorail...Ch. 12.2 - Prob. 30ECh. 12.2 - Prob. 31ECh. 12.2 - Prob. 32ECh. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - Profit: Smartphones (Compare Exercise 27.)...Ch. 12.2 - Projected Profit: Smartphones (Compare Exercise...Ch. 12.2 - Prob. 37ECh. 12.2 - Profit Because of sales by a competing company,...Ch. 12.2 - Prob. 39ECh. 12.2 - Metal Drums A company manufactures cylindrical...Ch. 12.2 - Tin Cans A company manufactures cylindrical tin...Ch. 12.2 - Prob. 42ECh. 12.2 - Prob. 43ECh. 12.2 - Prob. 44ECh. 12.2 - Box Design A packaging company is going to make...Ch. 12.2 - Prob. 46ECh. 12.2 - Prob. 47ECh. 12.2 - Carry-on Dimensions American Airlines requires...Ch. 12.2 - Prob. 49ECh. 12.2 - Prob. 50ECh. 12.2 - Package Dimensions The U.S. Postal Service (USPS)...Ch. 12.2 - Prob. 52ECh. 12.2 - Prob. 53ECh. 12.2 - Cellphone Revenues (Refer to Exercise 53.) If we...Ch. 12.2 - Prob. 55ECh. 12.2 - Prob. 56ECh. 12.2 - Prob. 57ECh. 12.2 - Prob. 58ECh. 12.2 - Prob. 59ECh. 12.2 - Prob. 60ECh. 12.2 - Average Profit The FeatureRich Software Company...Ch. 12.2 - Prob. 62ECh. 12.2 - Prob. 63ECh. 12.2 - Resource Allocation Your company is the largest...Ch. 12.2 - Prob. 65ECh. 12.2 - Prob. 66ECh. 12.2 - Prob. 67ECh. 12.2 - Prison Population The prison population in the...Ch. 12.2 - Prob. 69ECh. 12.2 - Prob. 70ECh. 12.2 - Prob. 71ECh. 12.2 - Prob. 72ECh. 12.2 - Prob. 73ECh. 12.2 - Prob. 74ECh. 12.2 - Prob. 75ECh. 12.2 - Agriculture Two years ago, your orange orchard...Ch. 12.2 - Prob. 77ECh. 12.2 - Prob. 78ECh. 12.2 - Prob. 79ECh. 12.2 - Prob. 80ECh. 12.2 - Prob. 81ECh. 12.2 - Prob. 82ECh. 12.2 - Prob. 83ECh. 12.2 - Prob. 84ECh. 12.2 - Prob. 85ECh. 12.2 - Explain how you would solve an optimization...Ch. 12.3 - In Exercises 1-10, calculate d2ydx2. [HINT: See...Ch. 12.3 - Prob. 2ECh. 12.3 - In Exercises 1-10, calculate d2ydx2. [HINT: See...Ch. 12.3 - Prob. 4ECh. 12.3 - In Exercises 1-10, calculate d2ydx2. [HINT: See...Ch. 12.3 - Prob. 6ECh. 12.3 - In Exercises 1-10, calculate d2ydx2. [HINT: See...Ch. 12.3 - In Exercises 1-10, calculate d2ydx2. [HINT: See...Ch. 12.3 - In Exercises 1-10, calculate d2ydx2. [HINT: See...Ch. 12.3 - Prob. 10ECh. 12.3 - In Exercises 1116 the position s of a point (in...Ch. 12.3 - In Exercises 1116 the position s of a point (in...Ch. 12.3 - Prob. 13ECh. 12.3 - In Exercises 1116 the position s of a point (in...Ch. 12.3 - In Exercises 1116 the position s of a point (in...Ch. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - Prob. 18ECh. 12.3 - Prob. 19ECh. 12.3 - Prob. 20ECh. 12.3 - Prob. 21ECh. 12.3 - Prob. 22ECh. 12.3 - In Exercises 1724 the graph of a function is...Ch. 12.3 - Prob. 24ECh. 12.3 - Prob. 25ECh. 12.3 - Prob. 26ECh. 12.3 - Prob. 27ECh. 12.3 - Prob. 28ECh. 12.3 - Prob. 29ECh. 12.3 - Prob. 30ECh. 12.3 - Prob. 31ECh. 12.3 - Prob. 32ECh. 12.3 - Prob. 33ECh. 12.3 - In Exercises 3344, find the x-coordinates of all...Ch. 12.3 - Prob. 35ECh. 12.3 - Prob. 36ECh. 12.3 - Prob. 37ECh. 12.3 - Prob. 38ECh. 12.3 - Prob. 39ECh. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Prob. 42ECh. 12.3 - Prob. 43ECh. 12.3 - Prob. 44ECh. 12.3 - Prob. 45ECh. 12.3 - Prob. 46ECh. 12.3 - Prob. 47ECh. 12.3 - Prob. 48ECh. 12.3 - Prob. 49ECh. 12.3 - Prob. 50ECh. 12.3 - Prob. 51ECh. 12.3 - Prob. 52ECh. 12.3 - Prob. 53ECh. 12.3 - Prob. 54ECh. 12.3 - Acceleration on Mars If a stone is dropped from a...Ch. 12.3 - Prob. 56ECh. 12.3 - Motion in a Straight Line The position of a...Ch. 12.3 - Motion in a Straight Line The position of a...Ch. 12.3 - Bottled Water Sales Annual sales of bottled water...Ch. 12.3 - Bottled Water Sales Annual U.S. per capita sales...Ch. 12.3 - Embryo Development The daily oxygen consumption of...Ch. 12.3 - Embryo Development The daily oxygen consumption of...Ch. 12.3 - Inflation The following graph shows the...Ch. 12.3 - Prob. 64ECh. 12.3 - Inflation The following graph shows the...Ch. 12.3 - Inflation The following graph shows the...Ch. 12.3 - Prob. 67ECh. 12.3 - Scientific Research: 19832003 The percentage of...Ch. 12.3 - Prob. 69ECh. 12.3 - Prob. 70ECh. 12.3 - Prob. 71ECh. 12.3 - Prob. 72ECh. 12.3 - Epidemics The following graph shows the total...Ch. 12.3 - Prob. 74ECh. 12.3 - Prob. 75ECh. 12.3 - Prob. 76ECh. 12.3 - Prob. 77ECh. 12.3 - Prob. 78ECh. 12.3 - Prob. 79ECh. 12.3 - Prob. 80ECh. 12.3 - Oil Imports from Mexico Daily oil production in...Ch. 12.3 - Oil Imports from Mexico Repeat Exercises 81 using...Ch. 12.3 - Prob. 83ECh. 12.3 - Prob. 84ECh. 12.3 - Prob. 85ECh. 12.3 - Prob. 86ECh. 12.3 - Prob. 87ECh. 12.3 - Prob. 88ECh. 12.3 - Prob. 89ECh. 12.3 - Prob. 90ECh. 12.3 - Prob. 91ECh. 12.3 - Prob. 92ECh. 12.3 - Prob. 93ECh. 12.3 - Prob. 94ECh. 12.3 - Prob. 95ECh. 12.3 - Prob. 96ECh. 12.3 - Prob. 97ECh. 12.3 - Prob. 98ECh. 12.4 - In Exercises 126, sketch the graph of the given...Ch. 12.4 - In Exercises 126, sketch the graph of the given...Ch. 12.4 - In Exercises 126, sketch the graph of the given...Ch. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12.4 - Prob. 6ECh. 12.4 - Prob. 7ECh. 12.4 - Prob. 8ECh. 12.4 - Prob. 9ECh. 12.4 - Prob. 10ECh. 12.4 - Prob. 11ECh. 12.4 - Prob. 12ECh. 12.4 - In Exercises 126, sketch the graph of the given...Ch. 12.4 - Prob. 14ECh. 12.4 - Prob. 15ECh. 12.4 - Prob. 16ECh. 12.4 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - Prob. 19ECh. 12.4 - In Exercises 126, sketch the graph of the given...Ch. 12.4 - Prob. 21ECh. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - Prob. 25ECh. 12.4 - Prob. 26ECh. 12.4 - Prob. 27ECh. 12.4 - Prob. 28ECh. 12.4 - Prob. 29ECh. 12.4 - Prob. 30ECh. 12.4 - Prob. 31ECh. 12.4 - Prob. 32ECh. 12.4 - Prob. 33ECh. 12.4 - Prob. 34ECh. 12.4 - Consumer Price Index The following graph shows the...Ch. 12.4 - Prob. 36ECh. 12.4 - Prob. 37ECh. 12.4 - Prob. 38ECh. 12.4 - Average Cost: iPhone Assume that is costs Apple...Ch. 12.4 - Average Cost: PlayStation 4s Assume that it costs...Ch. 12.4 - Prob. 41ECh. 12.4 - Subprime Mortgage Debt during the Housing Bubble...Ch. 12.4 - Prob. 43ECh. 12.4 - Prob. 44ECh. 12.4 - Prob. 45ECh. 12.4 - Prob. 46ECh. 12.4 - Prob. 47ECh. 12.4 - Prob. 48ECh. 12.4 - Prob. 49ECh. 12.4 - Prob. 50ECh. 12.5 - Rewrite the statements and questions in Exercises...Ch. 12.5 - Rewrite the statements and questions in Exercises...Ch. 12.5 - Rewrite the statements and questions in Exercises...Ch. 12.5 - Rewrite the statements and questions in Exercises...Ch. 12.5 - Prob. 5ECh. 12.5 - Prob. 6ECh. 12.5 - Prob. 7ECh. 12.5 - Prob. 8ECh. 12.5 - Sunspots The area of a circular sunspot is growing...Ch. 12.5 - Puddles The radius of a circular puddle is growing...Ch. 12.5 - Prob. 11ECh. 12.5 - Prob. 12ECh. 12.5 - End of the Earth In 5 billion years the Sun will...Ch. 12.5 - Prob. 14ECh. 12.5 - Sliding Ladders The base of a 50-foot ladder is...Ch. 12.5 - Prob. 16ECh. 12.5 - Prob. 17ECh. 12.5 - Prob. 18ECh. 12.5 - Prob. 19ECh. 12.5 - Average Cost Repeat Exercise 19, using the revised...Ch. 12.5 - Prob. 21ECh. 12.5 - Supply The number of retro portable CD players you...Ch. 12.5 - Revenue You can now sell 50 cups of lemonade per...Ch. 12.5 - Prob. 24ECh. 12.5 - Prob. 25ECh. 12.5 - Oil Expenditures Daily oil imports to the United...Ch. 12.5 - Resource Allocation Your company manufactures...Ch. 12.5 - Prob. 28ECh. 12.5 - Prob. 29ECh. 12.5 - Prob. 30ECh. 12.5 - Prob. 31ECh. 12.5 - Demand The demand equation for rubies at Royal...Ch. 12.5 - Prob. 33ECh. 12.5 - Prob. 34ECh. 12.5 - Baseball A baseball diamond is a square with side...Ch. 12.5 - Prob. 36ECh. 12.5 - Movement along a Graph A point on the graph of...Ch. 12.5 - Prob. 38ECh. 12.5 - Prob. 39ECh. 12.5 - Prob. 40ECh. 12.5 - Prob. 41ECh. 12.5 - Prob. 42ECh. 12.5 - Cones A right circular conical vessel is being...Ch. 12.5 - More Cones A circular conical vessel is being...Ch. 12.5 - Prob. 45ECh. 12.5 - Prob. 46ECh. 12.5 - Prob. 47ECh. 12.5 - Computers vs. Income Refer back to the model in...Ch. 12.5 - Prob. 49ECh. 12.5 - Prob. 50ECh. 12.5 - Prob. 51ECh. 12.5 - Prob. 52ECh. 12.5 - Prob. 53ECh. 12.5 - Prob. 54ECh. 12.5 - Prob. 55ECh. 12.5 - Prob. 56ECh. 12.5 - Prob. 57ECh. 12.5 - Prob. 58ECh. 12.5 - Prob. 59ECh. 12.5 - Prob. 60ECh. 12.5 - Prob. 61ECh. 12.5 - Prob. 62ECh. 12.6 - Demand for Oranges The weekly sales of Honolulu...Ch. 12.6 - Demand for Oranges Repeat Exercise 1 for weekly...Ch. 12.6 - Demand for Smartphones Worldwide annual sales of...Ch. 12.6 - Prob. 4ECh. 12.6 - Prob. 5ECh. 12.6 - Monorail Services The demand for monorail service...Ch. 12.6 - Tissues The consumer demand equation for tissues...Ch. 12.6 - Bodybuilding The consumer demand curve for...Ch. 12.6 - T-Shirts The Physics Club sells E=mc2 T-shirts at...Ch. 12.6 - Comics The demand curve for original Iguanawoman...Ch. 12.6 - E-Readers The demand for Amazons Kindle e-reader...Ch. 12.6 - Monorail Service on Mars The demand for monorail...Ch. 12.6 - Corn In the 1930s the economist Henry Schultz...Ch. 12.6 - Demand for Fried Chicken A fried chicken franchise...Ch. 12.6 - Paint-By-Number The estimated monthly sales of...Ch. 12.6 - Prob. 16ECh. 12.6 - Prob. 17ECh. 12.6 - Prob. 18ECh. 12.6 - Hyperbolic Demand Functions A general hyperbolic...Ch. 12.6 - Quadratic Demand Functions A general quadratic...Ch. 12.6 - Modeling Linear Demand You have been hired as a...Ch. 12.6 - Modeling Linear Demand You have been hired as a...Ch. 12.6 - Modeling Exponential Demand As the new owner of a...Ch. 12.6 - Prob. 24ECh. 12.6 - Income Elasticity of Demand: Live Drama The...Ch. 12.6 - Prob. 26ECh. 12.6 - Income Elasticity of Demand: Broadband in 2010 The...Ch. 12.6 - Prob. 28ECh. 12.6 - Income Elasticity of Demand: Computer Usage in the...Ch. 12.6 - Prob. 30ECh. 12.6 - Prob. 31ECh. 12.6 - Price Elasticity of Supply Given a supply equation...Ch. 12.6 - Income Elasticity of Demand (based on a question...Ch. 12.6 - Prob. 34ECh. 12.6 - Prob. 35ECh. 12.6 - Prob. 36ECh. 12.6 - Prob. 37ECh. 12.6 - Prob. 38ECh. 12.6 - Prob. 39ECh. 12.6 - Prob. 40ECh. 12 - In Exercises 18, find all the relative and...Ch. 12 - Prob. 2RECh. 12 - Prob. 3RECh. 12 - Prob. 4RECh. 12 - Prob. 5RECh. 12 - Prob. 6RECh. 12 - Prob. 7RECh. 12 - Prob. 8RECh. 12 - Prob. 9RECh. 12 - Prob. 10RECh. 12 - Prob. 11RECh. 12 - Prob. 12RECh. 12 - Prob. 13RECh. 12 - Prob. 14RECh. 12 - Prob. 15RECh. 12 - Prob. 16RECh. 12 - Prob. 17RECh. 12 - Prob. 18RECh. 12 - Prob. 19RECh. 12 - Prob. 20RECh. 12 - Prob. 21RECh. 12 - Prob. 22RECh. 12 - Revenue Demand for the latest best-seller at...Ch. 12 - Prob. 24RECh. 12 - Prob. 25RECh. 12 - Prob. 26RECh. 12 - Office Space Although still a sophomore at...Ch. 12 - Prob. 28RECh. 12 - Box Design The sales department at...Ch. 12 - Prob. 30RECh. 12 - Prob. 31RECh. 12 - Prob. 32RECh. 12 - Prob. 33RECh. 12 - Prob. 34RECh. 12 - Elasticity of Demand (Compare Exercise 23.) Demand...Ch. 12 - Prob. 36RECh. 12 - Prob. 37RECh. 12 - Prob. 38RE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Consider the graphs of y = f(x) and y = g(x) in the given diagram y= f(x). y = g(x) Evaluate (f+g)(2) -5 Determine all for which g(x) < f(x) Determine all for which f(x) +3 = g(x)arrow_forwardI) For what value(s) of x does g(x) = -4? Separate multiple answers with commas as needed. J) Give the interval(s) of such that g(x) > 0. Use the union symbol between multiple intervals. K) Give the interval(s) of such that g(x) <0. Use the union symbol between multiple intervals.arrow_forwardneed help on Barrow_forward
- 4. Use the properties of limits to help decide whether each limit exists. If a limit exists, fi lim (2x²-4x+5) a) x-4 b) lim 2 x²-16 x-4x+2x-8arrow_forward7. The concentration of a drug in a patient's bloodstream h hours after it was injected is given by 0.17 h Ah= h²+2' Find and interpret lim A(h). Remember, the answers to word problems should always be given in a complete h→00 sentence, with proper units, in the context of the problem.arrow_forward#2arrow_forward
- 2. We want to find the inverse of f(x) = (x+3)² a. On the graph at right, sketch f(x). (Hint: use what you know about transformations!) (2 points) b. What domain should we choose to get only the part of f (x) that is one- to-one and non-decreasing? Give your answer in inequality notation. (2 points) - c. Now use algebra to find f¯¹ (x). (2 points) -4- 3- 2 1 -4 -3 -2 -1 0 1 -1- -2- --3- -4 -N- 2 3 4arrow_forward1. Suppose f(x) = 2 4 == x+3 and g(x) = ½-½. Find and fully simplify ƒ(g(x)). Be sure to show all x your work, write neatly so your work is easy to follow, and connect your expressions with equals signs. (4 points)arrow_forwardFind the ane sided limit lim 2 x+1-3x-3arrow_forward
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY