Other Math Answers

Find the curl Fgiven that Fx,y,z=3x^2i+2zj-xk.

Select one:

A. -2i-j

B. 2i+j

C. -2i+j

D. 2i-j

If ψ=2xz^4-x^2y, find |∇ψ| at point (2, -2, -1).

Select one:

A. 93

B. 293

Question 3 [10 marks]

Which of the following statements is true about the given function?

(1) The Intermediate Value Theorem does not hold between x = −1 and x = 1.

(2) The function has two roots in the interval [−2, 4].

(3) It will take at least 15 iterations of the bisection method to approximate the root between

x = −2/3 and x = 2 correct to 10−4

.

(4) It will take no more than 14 iterations for the bisection method to converge to the root between

x = −2/3 and x = 2 correct to 10−5

.

(5) The function has at least one singular point.

Question 2 [10 marks]

Which of the following statements about the given function is FALSE?

(1) the graph of the function has one point of inflection and has two relative extrema.

(2) The function has no absolute extremum.

(3) The graph of the function has two roots in the interval [0, 3.5]

(4) The function has a point of inflection point at x = 0.

(5) The function has a relative maximum point at x =

−2

3

and relative minimum point at x = 2.

Question 1 [10 marks]

To have an idea on whether we should apply the bisection method to determine the root of f(x) = 0

in a given interval, we may

(1) draw the graph of f(x) and observe the graphs then conclude

(2) check if f(x) and f

(x) are continuous then conclude

(3) apply the function f(x) to the endpoints of the given interval and check the sign of the corre-

sponding outputs.

(4) check if f(x) has a critical point in the given interval

(5) check if f(x) has a point of inflection in the given interval.

(For Questions 2 to 5)

Consider the function f(x) = x

3 − 2x

2 − 4x + 2.

Find an irrational number which lies between (i). 2 and 3 (ii). 19 and 19.01 (iii). -4 and -2

Find the complex Fourier series of the function f(x)=cosax where -π<x<π.

1. Convert each degree measure to radians. Leave answers in terms of π.

1. 15°

2. 330°

3. 480°

4. -120°

5. -315

Which goal defines a good problem