Part I: Numerical Integration
Evaluate the following integrals:
i. ∫4(1−?−4?3 +2?5)??
0
ii. ∫3(?2??)?? 0
a) Analytically
b) Multiple application of Trapezoidal rule n = 4. c)
Simpson’s 1/3 rule for n = 4.
d) Simpson’s 1/3 and Simpson’s 3/8 rule for n = 5. e)
Determine the true percent relative error.
23. Given a = 5, b = 4, c = 2, evaluate the following:
a) a//c
b) a % b
c) b **c
d) b *= c
27. Given the following
var_1 = 2.0
var_2 = "apple"
var_3 = 'orange'
var_4 = 4
Predict the output of the following statements or indicate that
there would be an error.
a) print (var_1)
b) print (var_2)
c) print ("var_3")
d) print (var_1 / var_4)
e) print (var_4 + var_3)
f) print (var_2...
1) Find the following indefinite integrals.
a) (4-3xsec^2 x)/x dx
b) (5 sin^ 3 x ) / (1+cosx)(1-cosx) dx
2) A particle starts from rest and moves along the x-axis from
the origin at t = 0 with acceleration
a(t) = 6 - 2t
(ms^-2) at time t. When and where will it come to rest.
Remember dvdt =
acceleration and dsdt = velocity
3) Use substitution to find the following integrals.
a) (9x)/ sqrt...
Evaluate the following integrals using trigonometric
identities
(a) intergal sin6 x cos3 x dx
(b) Z π/2
o
cos5 x dx
(c) Z
sin3
(
√
x)
√
x
dx
(d) Z
tsin2
t dt
(e) Z
tan2
θ sec4
θ dθ
(f) Z
x sec x tan x dx
(15) Evaluate each of the following integrals. (a) Z cos(x)
ln(sin(x)) dx (b) Z x arcsin(x 2 ) dx (c) Z 1 0 ln(1 + x 2 ) dx (d)
Z 1/4 0 arcsin(2x) dx
(16) Use the table of integrals to evaluate the integrals, if
needed. You may need to transform the integrand first.
(a) Z cos(4t) cos(5t)dt
(b) Z 1 cos3 (x) dx
(c) Z 1 x 2 + 6x + 9 dx
(d) Z 1 50 −...
A, B, C, D are all matricies
A = 2x3
1 2 −3
−1 4 5
,
B = 2x3
3 0 −1
1 2 1
, C = 2x2
2 5
1 2
,
D = 3x3
1 −1 1
2 −1 2
4 −3 4
Find each of the following or explain why it does not exist.
1) A + B,
2) 2A − 3B,
3) A + C,
4) A − C,
5) AC,
6) CA,
7)...
1. a. Evaluate the following limit: lim ?→4 ( 2? 3−128 √?−2 ) b. Find the number ? ???ℎ ?ℎ?? lim ?→−2 ( 3? 2+??+?+3 ?
2+?−2 ) exists, then find the limit