(Solved) xxxxx |||||x xx xx XX XX XX xx oo xxxx ooo XX XX XX XXX xxxxxx XX XX XX oo xx xxxx XX X XX XX xxxxx xxxxx xxxxxx xxxx XXX oooo XXX ooooo XXX XX XXX...

calculus assignment, need help with all questions, excluding maple questions

xxxxx
|||||x
xx
xx
XX
XX
XX
xx
oo
xxxx
ooo
XX
XX
XX
XXX
xxxxxx
XX
XX
XX
oo
xx
xxxx
XX
X
XX
XX
xxxxx
xxxxx
xxxxxx
xxxx
XXX
oooo
XXX
ooooo
XXX
XX
XXX
oooo
xxxx
XX
XXXX
xxxxx
xxxxx Math 1P97. Assignment 1 (4%). Due date: Monday, May 15, 6:45pm Studentâ€™s name:
Total mark: NOTE: Students are expected to complete ALL questions on the assignment. However, only a subset of
questions will be considered for marking. Marks will be deducted for incomplete assignments. Show all
1. Simplify the following expressions:
a) 2(x2 + 4x âˆ’ 12) + x2 + 11x + 30
=
x+6 b) 3x2 + 2xy âˆ’ y 2
xy âˆ’ 3y 2
=
âˆ’ 2 + 10 Â· 2
(3y + x)(x + y)
x âˆ’ 9y 2 c) 1 yâˆ’x
1 x 
yâˆ’
x âˆ’ 2
y
x
=
y 

1 xâˆ’y
1
2
xâˆ’
y âˆ’ 2
x
y  2 2. Find the domain of f (x):
a) f (x) = âˆš
3 xâˆ’1
;
| +1|
x2 âˆš
b) f (x) = x 16 âˆ’ x2 ; 2 24âˆ’x
c) f (x) =
.
xâˆ’2 3. Find the rules for the composite functions (g â—¦ f )(x) and (f â—¦ g)(x);
a) If f (x) = 5x and g(x) = x5 + 5x + 5; b) If f (x) = 4 âˆ’ 4x + x2 and g(x) = c) If f (x) = âˆš x2
,
xâˆ’4 x2 + 1 and g(x) = ln x. 4. (Maple Question) An office building worth \$16, 166, 050 million when completed in 1980 was depreciated linearly over 50 years to \$10, 000, 000.
a) Express the book value of the building V (n) as a function of year starting from 1980: n =
0, V (0) = 16, 166, 050. b) Build a graph of the function V = V (x), x âˆˆ [0, 50] and find the book value of the building in
2017 using Maple. Attach the Maple worksheet. c) Find the rate at which the building is being depreciated each year. 5. Find the indicated limits, if they exist.
a) e3x (x + 4)
=
xâ†’0 x2 + 6x âˆ’ 16
lim 2x2 âˆ’ 3x âˆ’ 2
b) lim 2
=
xâ†’2 x + x âˆ’ 6 c) d) 1 âˆ’ 3x2 + 5x5
âˆš
=
xâ†’âˆž
1 + x10
lim âˆš lim
xâ†’âˆž e) x2 + 5x âˆ’
7 âˆš x2 âˆ’ 9x = x4 + 10x3 + 16x2
=
xâ†’âˆ’2
x4 âˆ’ 16
lim 6. Let f =  4 âˆ’ x2 ,
x3 âˆ’ 2x2 + a, if x â‰¤ 2
Find the value of a that will make f continuous on (âˆ’âˆž, âˆž).
if x &gt; 2 8. (Commissions, problem 68) The base monthly salary of a salesman working on commission is \$26, 000.
For each \$50, 000 of sales beyond \$100, 000, he is paid a \$1000 commission.
a) Sketch a graph y = f (x), x âˆˆ [100, 300] showing his earnings y as a function of the level of his
sales x (in thousands). b) Determine the values of x for which the function f is discontinuous and find their one-sided
limits. 9. (Energy expended by a fish, problem 72) Suppose a fish swimming a distance of L ft at a speed of
Ï… ft/sec relative to the water and against a current flowing at the rate of u ft/sec (u &lt; Ï…) expends
a total energy given by
aLÏ… 3
E(Ï…) =
,
Ï…âˆ’u
where E is measured in foot-pounds (ft-lb) and a is a constant.
a) Evaluate lim E(Ï…) and interpret your result.
Ï…â†’u+ b) Evaluate lim E(Ï…) and interpret your result.
Ï…â†’âˆž

Solution details:
STATUS
QUALITY
Approved

This question was answered on: Sep 05, 2019

Solution~000200199960.zip (25.37 KB)

This attachment is locked

We have a ready expert answer for this paper which you can use for in-depth understanding, research editing or paraphrasing. You can buy it or order for a fresh, original and plagiarism-free solution (Deadline assured. Flexible pricing. TurnItIn Report provided)

STATUS

QUALITY

Approved

Sep 05, 2019

EXPERT

Tutor