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...

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 correct 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 correct 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 correct 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 correct option is D
Velocity = -gt= -9.8*5 = -49
But speed is not a vector quantity and it is always positive
Hence correct option is C
F(x+h)= 3-(x+h)^2 = 3-x^2-2xh-h^2
Hence correct option is D
For f= x^n
Df/dx = nx^n-1
Using same formula dy/dx = -24x^3-14x
Hence correct option is A
Using differentiation rule for fraction
Which is
2
2
2
( )* * ( )
4(3 2) 3(4...