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Assestment I 1. The domain of f(x) = .,112,c2 in interval notation is: a. [41,11] b. (0, ) c. (11, ) d. (-11,11) 2. Given f(x) = 6—x and g(x) = 2x2+x, find (g0 f)(-2) a. -4 b. 0 c. 36 d. 136 3. Write...

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Assestment I
1. The domain of f(x) = .,112,c2 in interval notation is: a. [41,11] b. (0, ) c. (11, ) d. (-11,11)
2. Given f(x) = 6—x and g(x) = 2x2+x, find (g0 f)(-2) a. -4 b. 0 c. 36 d. 136
3. Write an equation for a function that has a graph with the given characteristics. The shape of x2, but upside down and shifted right 5 units. a. y = —x2-5 b. y = —(x-5)2 c. y = —(x+5)2 d. y = —x2+5
4. Express In XXXXXXXXXXin terms of In(2) and In(3). a. -41n(2) + In(3) b. In(3/16) c. -In(3) + 41n(2) d. none of these
5. Use a reference triangle to find tan-1(-4T). a. —27—t- / 3 b. —,r/3 c. 2-c/3 d. 2,r/3
005_f5ie85k-vvxomseq.pdf
Answered Same Day Dec 29, 2021

Solution

David answered on Dec 29 2021
118 Votes
Solution
Solutions ARE HIGHLIGHTED
Now square root exist only for positive numbers and hence function
inside the square root must be positive
So
121-x2 >=0
x2 <= 121
x [-11,11]
option A
Gof(x) = replace x by f(x) in g(x)
So gof(x) = 2* f(x)2 +f(x)
Putting -2
F(-2)= 6—2 = 8
Hence gof(-2) = 2*64+8 = 136
Option D
Upside down so and shape of x^2
Y= -(x-a)2
Shifted right 5 unit so Y is zero when x= 5
Hence Y= -(x-5)2
And Option B
Ln(0.1875)
.1875 = 1875/10000 = 25*25*3/25*25*16= 3/16
Ln(3/16)= ln3 -ln 16 = ln 3- 4ln2
Hence option A
tan(60)= sqrt(3)
hence angle is – 60
option B
Take 1998 as base ear
Let Population = C*exp(at)
C= 1225
At t=5 after 5 year population is 2340
C*exp(5a)= 2340
Exp(5a)= 2340/1225, a=0.1294
Population in 2008
C*exp(10a)= 1225 *exp(10a)= 4470
Hence co
ect option B
Rate of change = 12x^2
Average of rate of change=
6
2
4
3 6
4
[ 12 ] / 2
[4 ] / 2 608 / 2 304
x dx
x  

Hence Option C
Option D does not exists
Using L hospital rule and differentiating both numerator and
denomerator we get
0
0
0
2 1 1
2
2 2 1
1
1
1
2 1
x
x
x
x
Lim
x
x
Lim
Lim
x



 



Option B
Take a=sqrt(9theta)
Now when theta tends to zero a also tends to zero
And hence it is reduced to
0
9sin( )
9a
a
Lim
a
  Hence co
ect option D
Dividing numerator and denominator by x^5 we gwt
4 / 7 / ^ 2 4 / ^ 5
0
7
x
x x x
Lim 
 

Hence as x tends to infinity 1/x tends to zero
So co
ect option is A
This function has only a vertical asymptote at x=2
Hence option D
Slope dy/dx= -12x = -60
Hence line is y= -60x +c
Putting point (5,-147) we get c= 153
Hence co
ect option is D
Velocity = -gt= -9.8*5 = -49
But speed is not a vector quantity and it is always positive
Hence co
ect option is C
F(x+h)= 3-(x+h)^2 = 3-x^2-2xh-h^2
Hence co
ect option is D
For f= x^n
Df/dx = nx^n-1
Using same formula dy/dx = -24x^3-14x
Hence co
ect option is A
Using differentiation rule for fraction
Which is
2
2
2
( )* * ( )
4(3 2) 3(4...
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