+61-413 786 465

info@mywordsolution.com

 Algebra Math Calculus Physics Chemistry Biology Earth Science Physiology History Humanities English Sociology Nursing Science

Home >> Math

Answer all problems showing all working.

1) Find the equation of the tangent line to the curve y=2x-x3 at the point (1,1).
2) Evaluate the derivative of the function below from first principles.

f(x)=(x2-2x/x2-x-2)

3) In this exercise we estimate the rate at which the total personal income is rising in the Richmond-Petersburg, Virginia, metropolitan area.In 1999, the population of this area was 961, 400, and the population was increasing at roughly 9200 people per year. The average annual income was \$30, 593 per capita, and this average was increasing at about \$1400 per year. Use the Product Rule and these figures to estimate he rate at which total personal income was rising in the Richmond-Petersburg area in 1999. describe the meaning of each term in the Product Rule.

4) Let f(x)= x4-2x2

a) Use the definition of a derivative to find f'(x) and f''(x)

b) On what intervals is f(x) increasing or decreasing?

c) On what intervals is f(x) concave upward or concave downward?

5) Differentiate

a) y= (1+sinx)/(x+cosx)

b) √x+√y=1

6) Sketch the graph of a function that satisfies all of the given conditions:

a) f’(x) > 0 if x < 2; f’(x) > 0 if x > 2; f’(2) = 0

b) f’’(x) < 0 if x < 2; f’’(x) < 0 if x >2; f not differentiable at x = 2

7) Evaluate the radical expression and express the result in the form a + bi.

a) √(-9/4)

b) √1/3(√-27)

8) Find all solutions of the equation and express them in the form a + bi.

a) x2=1/2x+1=0

b) z+4+12/z=0

9) prepare the complex number in polar form with argument θ between 0 and 2π

a) 3i(1 + i)

b)√2 + √2i

10) prepare z1 and z2 in polar form. Find the product z1z2 and the quotients z1/z2 and 1/z1. Leave your answer in polar form.

a) z1= 4√3 - 4i       z2=8i

b) z1=3+4i             z2=2-2i

11) Utilising De Moivre’s theorem to evaluate the following

a) (1-√3i)5

b) (-1/2 -√3/2)15

• Category:- Math
• Reference No.:- M9584

Have any Question?

## Related Questions in Math

### Questions -q1 prove the following identitiesa sinx y sinx

Questions - Q1. Prove the following identities a. sin(x + y) + sin(x - y) = 2 sin x cos y b. sec(x - y) = cos(x + y)/(cos 2 x - sin 2 y) c. tan 2 x - sin 2 x = (tan x sin x) 2 Q2. Solve the following equations for x ∈ [0 ...

### Question 1 - for the ivp of ode y t-1e-y y1 0 find an

Question 1 - For the I.V.P of ODE y' = (t-1)e -y , y(1) = 0, find an approximation to y(1.2) using the following numerical methods with Δt = 0.1. Compare the numerical solution with the exact solution and compute the err ...

### Assignment - provide solution to the following questionsq1

Assignment - Provide solution to the following questions: Q1. Evaluate the following: ∫xsin3x dx Q2. If , then for what value of α is A an identity matrix? Q3. The line y = mx + 1 is a tangent to the curve y 2 = 4x. Find ...

### Questions - provide solution to the following questionsq1

Questions - Provide solution to the following questions: Q1. Evaluate the following: ∫xsin3xdx Q2. If , then for what value of α is A an identity matrix? Q3. The line y = mx + 1 is a tangent to the curve y 2 = 4x. Find t ...

### Assessment taskpractical investigation- question 1 requires

Assessment Task Practical Investigation - Question 1 requires selecting reference points from the graph. It is expected that each student will choose different reference points to other students. Take note of the criteri ...

### Question 1 what is the nth order approximation using taylor

Question: 1. What is the nth order approximation using Taylor series? 2. What is Error Propagation? 3. Please explain what the total numerical error is? Please illustrate how the change of step size will affect the total ...

### Question you will recommend a course of action regarding

Question: You will recommend a course of action regarding strategic planning in light of the issue the healthcare organization is facing. Be sure to address the following: 1. Provide a brief summary of the issue facing t ...

### Assignment -question 1 let t and or 0 1 be a boolean

Assignment - Question 1. Let (T, ∧, ∨,', 0, 1) be a Boolean Algebra. Define ∗ : T × T → T and o : T × T → T as follows: x ∗ y := (x ∨ y)' x o y := (x ∧ y)' (a) Show, using the laws of Boolean Algebra, how to define x ∗ y ...

### Maths assignment - 1 analysis of a data setusing a

Maths Assignment - 1. Analysis of a data set Using a continuous data set you are requested to collect in the types of data and gathering data section, perform a statistical analysis on your data. You have opportunities t ...

### Mathematics- algebraic geometry problemlet k denotes an

Mathematics- Algebraic Geometry Problem Let K denotes an algebraically closed field and let P 1 be constructed as in Example 5.5(a) in Gathmanns notes, i.e. P 1 is the gluing of X 1 = A 1 and X 2 = A 1 along  the open su ...

• 13,132 Experts

## Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

### Why might a bank avoid the use of interest rate swaps even

Why might a bank avoid the use of interest rate swaps, even when the institution is exposed to significant interest rate

### Describe the difference between zero coupon bonds and

Describe the difference between zero coupon bonds and coupon bonds. Under what conditions will a coupon bond sell at a p

### Compute the present value of an annuity of 880 per year

Compute the present value of an annuity of \$ 880 per year for 16 years, given a discount rate of 6 percent per annum. As

### Compute the present value of an 1150 payment made in ten

Compute the present value of an \$1,150 payment made in ten years when the discount rate is 12 percent. (Do not round int

### Compute the present value of an annuity of 699 per year

Compute the present value of an annuity of \$ 699 per year for 19 years, given a discount rate of 6 percent per annum. As