1. Sketch each polynomial function: a) y=(x-2)³-3 b) y=-2x²(x+3) c) y=(x+1)(x−2)² d) y=x²-13x² +36
1. Sketch each polynomial function: a) y=(x-2)³-3 b) y=-2x²(x+3) c) y=(x+1)(x−2)² d) y=x²-13x² +36
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help me with questions 1,2,10, 21, 22 and 28(part 2). Please show work
![1. Sketch each polynomial function:
2.
3.
5.
6.
8.
9.
a) y==(x-2)³-3 b) y=−2x²(x+3) c) y=(x+1)(x− 2)³
d) y=x²-13x² +36
Given y = f(x)
a) State the degree of the function.
b) State the coordinates of the zeros, local minimums
and local maximums.
10.
c) State the intervals of increasing and decreasing.
d) Find the equation of the function
Find the cubic polynomial function with two of its zeros 2 and -3+√2, y-intercept of 7.
7. a) Find the value of kif 2x³ − 4x² − 3x + k is divisible by 2x-3
b) Given ax³ + x²+x+b, find the value of a and b if the remainder when divided by
(x-1) and (x+1) are 6 and 2 respectively.
State the equations of the asymptotes for each curve:
2x³ + x² +5
b) y =
x²
3x
a) Find the quotient and the remainder when 3x² - 4x +3 is divided by x-2.
b) Find the value of k in x³ - 2x² + kx-3 if (x+3) is a factor.
Factor a) x³-4x² - 4x+16 b) 8x³+27 c) 5x³ +3x²-12x+4 d) x¹-11x² +18
Solve each: a) 2x³ + x²-18x-9=0
b) x(x² +9x+3)= −5(2x+1)
c) -2x(x+3)(x-2)(x-5) <0 d) -x³-5x² +6x20
a) y = 2
Given y=x²-2x+3
a) Find the average rate of change of y with respect to x in the interval [-2, 3]
b) Estimate the slope of the tangent to the curve at x = 3
c) Find the equation of the tangent at at x =2.
2x+6
x-3
2x²-18
x²+x-12
c) y = 2
x² -4
e) y = 2*¹ - 3
Analyze each rational function the sketch the graph.
a)
y =
b) y=-
1,30
4
30-1
10-
d) y =
30)
(5-6)
r+5r-1
x+2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d431b6f-2241-4e16-9a30-9ef04cc22547%2F192cb339-73af-46cf-9ef1-26a01987654b%2F5huxmu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Sketch each polynomial function:
2.
3.
5.
6.
8.
9.
a) y==(x-2)³-3 b) y=−2x²(x+3) c) y=(x+1)(x− 2)³
d) y=x²-13x² +36
Given y = f(x)
a) State the degree of the function.
b) State the coordinates of the zeros, local minimums
and local maximums.
10.
c) State the intervals of increasing and decreasing.
d) Find the equation of the function
Find the cubic polynomial function with two of its zeros 2 and -3+√2, y-intercept of 7.
7. a) Find the value of kif 2x³ − 4x² − 3x + k is divisible by 2x-3
b) Given ax³ + x²+x+b, find the value of a and b if the remainder when divided by
(x-1) and (x+1) are 6 and 2 respectively.
State the equations of the asymptotes for each curve:
2x³ + x² +5
b) y =
x²
3x
a) Find the quotient and the remainder when 3x² - 4x +3 is divided by x-2.
b) Find the value of k in x³ - 2x² + kx-3 if (x+3) is a factor.
Factor a) x³-4x² - 4x+16 b) 8x³+27 c) 5x³ +3x²-12x+4 d) x¹-11x² +18
Solve each: a) 2x³ + x²-18x-9=0
b) x(x² +9x+3)= −5(2x+1)
c) -2x(x+3)(x-2)(x-5) <0 d) -x³-5x² +6x20
a) y = 2
Given y=x²-2x+3
a) Find the average rate of change of y with respect to x in the interval [-2, 3]
b) Estimate the slope of the tangent to the curve at x = 3
c) Find the equation of the tangent at at x =2.
2x+6
x-3
2x²-18
x²+x-12
c) y = 2
x² -4
e) y = 2*¹ - 3
Analyze each rational function the sketch the graph.
a)
y =
b) y=-
1,30
4
30-1
10-
d) y =
30)
(5-6)
r+5r-1
x+2
Transcribed Image Text:21.
22.
24
25.
26.
27.
28.
For each, state the amplitude, period, phase shift and sketch the graph.
-cos(2x + = +1
2
a) y = 2 sin
3
State the equation of each sine function.
b)
a)
amplitude of 3.5,
27
period of
5
I
phase shift of
4
b) y=-cos 2x +
ww
114
Evaluate without a calculator.
1
a) log
b) log, 625
Simplify: a) log, √a
e) (log 10 (log a + 2 log b)
12 500
*
b) log.
c) y = 2cosx+5
The average monthly temperature, T, in degrees Celsius, for any month, t, for the town
of Someplace, is modelled by the function 7(t)=19.1 sin
+7.5. For t=0, the
6
B
month is January.
a) What is the maximum average monthly temperature?
b) What is the period of the function and what does it mean?
c) Determine the month with minimum average monthly temperature.
d) When is the average monthly temperature about 24°C.
+42+7.5.
+4.2
A pedal on a bicycle has an arm length of 20 cm and rotates about an axle 32 cm above
the ground. If the pedal states at its lowest point and rotates at 20 revolutions every
minute, find a sinusoidal function that will model the height h, in centimetres, of the
pedal after t seconds. At what time during the first 5 seconds will the pedal be 40 cm
above the ground?
L 18 48 50 44 24
c) log, 32 d) log 0.001 e) log 25-log-
C) 430g.x
d) 3 log 2x-5log x + 2log 2
For each function:
i) State the domain and range ii) sketch the graph iii) state the equation of its inverse
a) y=-2log, (x+1)
d) y=1+ log₂ (x-4)
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