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Calculus 180. just try to do well in this test. I need your help please and thanks. Just give answers these question. take time give me good answer.
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Math 180 -Assignment #3
Due: 10:00a, Monday, March 1st, 2021
**************************************************************************
READ AND FOLLOW DIRECTIONS
**Complete solutions using proper notation will be required to receive full credit.
*Please clearly identify your final answers. Circle your final answers where appropriate.
**Please start each NUMBERED PROBLEM on a new page.
*Please put your problems in numerical order before submitting them as a single PDF or
Word Document via Blackboard.
**Do NOT wait until the last minute. Late submissions will receive severe reductions.
*Each numbered problem will be graded on a 10-point scale. The total will be scaled to 100
points.
*****************************************************************************
#1.) Given 35 xy + 4 x 2 = 9 x + 6 y + 53,
dy
using Implicit Differentiation.
dx
b.) Find the equation of the line tangent when x = 1.
a.) Find
#2.) Choose ONE of the following:
A.) An airplane is flying at a constant speed at an altitude of 10,000 ft on a line that will take it
directly over an observer on the ground. At a given instant, the observer notes the angle of
1
elevation of the airplane is radians and is increasing at a rate of
radian/sec. Find the speed
3
60
of the plane.
B.) A water tank is in the shape of an inverted cone that measures 4 feet across the top and has
3
a depth of 10 feet. Water is being pumped into the tank at a rate of
cubic feet per minute.
5
How fast is the water level rising when the depth of the water is 4 feet.
C.) The supply equation for a certain commodity is x = 1000 3 p 2 + 20 p , where x units are
supplied per month when p dollars is the price per unit. Find the rate of change in the supply if
the current price is $20 per unit and the price is increasing at the rate of $0.50 per month.
1
#3.) Given f ( x ) = x4 − x2 + 2, − 3,4 .
8
a.) Find the critical numbers.
b.) Identify the extrema.
#4.) Consider a function, f ( x ) , whose domain is x 0 and f ' ( x ) =
−8 ( x − 4 )
2
1
x 3 ( x + 3)
a.) Find the critical numbers.
b.) Identify the open intervals where the graph of f ( x ) is increasing/decreasing.
c.) Identify any relative extrema.
#5.) Consider a function, f ( x ) , where f '' ( x ) =
−2 ( 2 x − 7 )
1
x 3
( x + 3)
.
You may assume that f ( x ) and f ' ( x ) are defined for all values of x.
a.) Identify the open intervals where the graph of f ( x ) is concave up/down.
b.) Identify any points of inflection.
#6.) Choose A or B, but not both. Evaluate the limit. ( Remember, this is a calculus course.)
−12 x + 7
−12 x2 + 3x + 7
A.)
lim
B.)
lim
x→ 3 3
x →−
4 x2 − 5
8x + 4
#7.) Create ONE rational function that has ALL of the following features listed below:
−The function has the x-intercepts: ( 2,0 ) , ( − 3,0 ) , ( 5,0 )
−The function has the vertical asymptotes: x = 1, x = −1
2
−The function has a horizontal asymptote: y = −
3
− Write your rational function where the numerator and denominator are factored.
-NOTE: There are multiple correct answers to this problem.
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