Description
I’m working on a calculus practice test/quiz and need the explanation and answer to help me learn.Write your solutions neatly, legibly, and in a well-organized manner. They must be clear to understand.Your solution must include your work and the final answer. Always show your work. Your work is more important than your final answer. Any results without showing steps might not be counted. makemake sure to use formulas in the Calculus 2 level.don’t miss any step.
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Name:
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1. (15pts) A population of dear inside a part has a carrying capacity of 200 and a growth rate of
2%. If the initial population is 50 deer, what is the population of dear at any given time? Here
are the instructions.
(a) This question is an example of the formula I derived in one of the lecture videos. DO NOT
use just the final formula. You must set up a differential equation and derive a final formula
by showing each step.
(b) You must use the given numbers. Do not use the letters like k and K. Those given numbers
must be a part of your work from the beginning of your work.
(c) Do not simplify your answer. If you copy a result from your calculator, it is automatically
wrong. Note only there is no credit for a calculator work, but also there will be points-off
because it is a wrong information.
(d) Place your final answer in a box.
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2. (10pts) Find the particular solution to 8y 0 = −2 cos(2x) − cos(4x) that passes through (π, π),
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1
given that y = C − sin(2x) −
sin(4x) is a general solution. Show your work and simplify
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your answer.
Answer:
3. (15pts) Find the solution of y 0 = ey 5x with y(0) = ln(ln 5). Show your work for each step and
simplify your answer. You need to write your final answer in a function form, i.e., write y as a
function of x.
Answer:
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4. (15pts) Find the solution of xy 0 + y = x ln x with y(1) = − 14 . Show your work for each step and
simplify your answer. You need to write your final answer in a function form, i.e., write y as a
function of x.
Answer:
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5. (15pts) Solve (1 + x)y 0 = (x + 2)(y − 1) with y(0) = 0. Show your work for each step and simplify
your answer. You need to write your final answer in a function form, i.e., write y as a function of
x.
Answer:
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6. (15pts) Solve (x + 2)y 0 = 3x + y with y(−1) = 6. Show your work for each step and simplify your
answer. You need to write your final answer in a function form, i.e., write y as a function of x.
Answer:
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k
7. (15pts) Find the orthogonal trajectories of the family of the curves y = where k is an arbitrary
x
constant. Identify the family of the orthogonal trajectories by simplifying your answer.
Answer:
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