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Assignment No. 1
MTH101 ( Spring 2015 )
Total marks: 20
Lectures: 01 to 18
Due date: June 8, 2015
DON’T MISS THESE Important instructions:
• There are Four Sections and Each section carries 20 marks.
• Solve all questions of ONLY THAT ONE SECTION which is directed in your
ANNOUNCEMENT page. If you do not solve the INSTRUCTED SECTION, your
marks will be deducted. See your ANNOUNCEMENT page.
• Solve your assignment in MS Word, using Math Type Software.
• File with jpg or other image files will be awarded ZERO marks.
SECTION 1 ( For the students with Section incharge Miss Zakia Rehmat.
Question: 1 Marks: 5 + 5
a) Solve the following inequality and write the solution in the form of intervals.
321
55
x −>
b) Find the domain and range of the following function.
2
1()
4
gz
z
=
−
Question: 2 Marks: 3 + 2
Consider the following function.
32
2()
36
xxfx
x
−
=
−
a)
Construct a table for the values of ()fx corresponding to the following values
of x and estimate the limits
2
lim ( )x
fx−
→
and
2
lim ( )x
fx+
→
respectively.
1.97,1.9997, 1.999997,1.98, 1.9998
2.02, 2.01, 2.0002, 2.0001, 2.000001
x
x
=
=
b)
Evaluate the limit 2
lim ( )x
fx→
algebraically.
Question: 3 Marks: 5
Write the function in the form of ()y fu= and ()u gx= , then find dy
dx
as a function of x.
4
5 cos sin cosy x xx−
= +
Hint: Use “CHAIN RULE” to solve it
SECTION 2 ( For the students registered with Section incharge Mr. Imran Talib )
Question: 1 Marks: 5 + 5
(a) Solve the following inequality and show the solution set on the real line.
4 2
3
x
x
+
br/>−
(b) Find the centre and radius of the circle with equation:
22
10 8 59 0xy xy+− +−=
Question: 2 Marks: 5 + 5
( ) graphed here, state whether the following limits exist or not?
If they exist then determine it .Moreover, if they do not exist then just
(a) For the following functi
ify the answer with appropriate r
o
e on
n
as .
s ft=
0
2
1
(I) lim ( )
(II) lim ( )
(III) lim ( )
t
t
t
ft
ft
ft
→
→
→
−
−
4 3 2 1 1 2
1.0
0.5
0.5
1.0
2
2
23
43
(b) Let ( ) xx
x
x
x
h −−
−+
=
3
(I) Make a table of the values of at 2.9 2.99 2.999 2.9999 and so on.Then estimate lim ( ).
What estimate do you arrive at if you evaluate at 3.1 3.01 3.001 and so on ?
,, , ,
,, ,
x
h x hx
hx
→
=
=
3
(II) Find lim ( ) algebraically.
x
hx
→
SECTION 3 ( For the students registered with Section incharge Mr Muhammad
Sarwar )
Question: 1 Marks: 5
Given that A (5, 1) and B (3, 4). Find
(i) Slope of line joining A and B,
(ii) Equation of line passing through A and B
Question: 2 Marks: 5
Find the center and radius of the circle with equation,
22
3 3 21 6 7 0x y xy+ − + +=
Question: 3 Marks: 5
Evaluate,
2
3
4 36lim
3x
x
x→
−
−
Question: 4 Marks: 5
Find the derivative of 2
() 1fx x= − by definition /
0
( ) ()( ) limh
fx h fxfx
h→
+−=
SECTION 4
( For the students registered with Section incharge Mr. Mansoor Khurshid )
Question: 1 Marks: 5
Find the slope and y-intercept of the line 3 12 27 0.xy− += Deduce the x-intercept from the
equation of the line.
Question: 2 Marks: 3 + 2
(a) What do you judge about the differentiability of ()fx x= at 0x = ?
Support your answer with explanations and reasoning.
(b) Write names of two functions which are continuous on the set of real numbers ( ) .. ,R ie −∞ ∞
Question: 3 Marks: 2 + 3
(a) Let ( ) 200hx = . Investigate the value of ()hx when x approaches to .∞
(b) Find tandx
dx sin x
Question: 4 Marks: 5
Find the derivative of the function tany sin x cos x sec x x= +− , using “CHAIN RULE”
(i.e., by using some appropriate substitution).
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