all working must be shown. Also need explanations of how you arrived at every answer. Particularly graphs.

Q.1 Use the properties of limits to help decide whether the limit exists. If the limit exists,
find its value.

xx
xx
x 76
153
lim
2
2




Solution: The limit does not exist for the expression:
The expression cannot be reduced and at the point given, function is not continuous.
Q.2 Find the limit, if it exists.

2
4
lim
2
2 

 x
x
x
Solution: The limit exists for the expression:
422)2(lim
)2(
)2)(2(
2
4
lim
2
2
2








x
x
xx
x
x
x
x

Q.3 Find the derivative:
y =
xx
28
3

Solution: Differentiating the function:
y =
3
228
x
x

6
24
6
424
6
223
2
3
2
2
2426244
)28)(3())(4(
)(
)(
3)('
)(
4)('
28)(
)(
)(')()()('
)(
)(
x
xx
x
xxx
x
xxxx
xg
xf
dx
d
xxg
xxg
xxf
xxf
xg
xgxfxgxf
xg
xf
dx
d























Q4. Find the equation of the line tangent to the graph of the function at the indicated
point. f(x) = x – x
2
at (-1, -2)
Solution: As we know, y’ is the slope of tangent line at a given point.
f(x) = x – x
2
f’(x) = 1- 2x
At x = -1, f(-1) = 3
So, the slope of tangent line at x = -1 is 3 and it passes through (-1, -2).
Thus, y = 6x + b where y = -2, and x = -1
-2 = 6(-1) + b
b = 4
y = 3x + 4
3x – y + 4 = 0
Q.5 Differentiate: f(x) = (3 – 8x)
230

Solution: Differentiating the function:
= 230(3 – 8x) . (-8)
= (690 – 1840x)(-8)
= (14720x – 5520)
Q.6 Differentiate f(x) =
512 xx 
Solution:...