maths

1. Prove using mathematical induction that 1+2+3+...+n=[ n(n+1)]/2

2. Find the derivative of 2^x^2+log2(2x^2-1)

3. Use DeMeoivre's theorem to simplify the following expressions

[(Cos pie/3 + isin pie/3)^5 (cos 2pie/3- isin 2pie/3)^4]/ (cos pie/6 - isin pie/6)^2

4.Find the radius of the circle with center at C (-2,5) if the line x+3y=9 is a tangent line.

5. Find the equation of the line of a circle if A(6,4) and B(-2,7) are the end points of the diameter.

6.(a). Let f(x)=x^4-x^2-2
(i) Find the relative maximum and minimum points of f(x).

(ii) Determine the intervals where the function is increasing.

(iii) Hence sketch the graph of the function.
(b) (i) sketch the graph of the function f(x)=x(2-x_ for values of x in the interval -2<_x<_4.

(ii) Find the area bounded by the curve f(x)=x(2-x) and the x- axis between the lines x= -1 and x=2.

7.Solve the equation (1-cos2A)/(3+cos2A)=1/7 for values of A in the interval 0<_ A <_180

8.(a) sketch the graph of f(x)= -2cos(x/2) for values of x in the interval 0<_ x <_ pie

(b) determine the general solution of -2cos(x/2)=0

9. The root of the equation 2x^2-4x+5=0 are a and b.

(i) Find the value of (1)/(a^2+1) + (1)/b^2+1

(ii) Find an equation whose roots are 2/a and 2/b.

asked by muselitata
  1. Wow,
    If I do this for you, will you forfeit the grade you will get and let me have it?

    classic case of homework dumping.

    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. maths

    1. Prove using mathematical induction that 1+2+3+...+n=[ n(n+1)]/2 2. Find the derivative of 2^x^2+log2(2x^2-1) 3. Use DeMeoivre's theorem to simplify the following expressions [(Cos pie/3 + isin pie/3)^5 (cos 2pie/3- isin
  2. Studying for Pre Cal exam

    Find the fourth roots of − 1/2 + (square root)3/2 i Write the roots in trigonometric form. A - w 1=cos(35°)+isin(35°) w2 =cos(125°)+isin(125°) w3 =cos(215°)+isin(215°) w4 =cos(305°)+isin(305°) B - w1
  3. maths

    Choose the two options which are true for all values of x 1) cos (x) = cos ( x – pie/2) 2) sin (x + pie/2) = cos (x – pie/2) 3) cos (x) = sin (x – pie/2) 4) sin (x) = sin (x + 4pie) 5) sin (x) = cos (x – pie/2) 6) sin^2
  4. Advance Math

    Find solutions of the equation in the interval [0, 2pie} Cos(x+pie/3)+Cos(x-pie/3)=1 I need to show work without calculator and be able to check in order for it to work Thanks for help
  5. Calculus

    Determine the polar form of the complex number 3 - 2i. Express the angle theta in degrees, where 0 < theta < 360°, and round numerical entries in the answer to two decimal places. 326.31(cos 326.31° – isin 326.31°)
  6. math

    evaluate the expressions below and leave them in radical form. 1. sin(pie symbol/6)csc(pie symbol/6) 2. sec(pie symbol/3)cos(pie symbol/3)+tan(pie symbol/3)cot(pie symbol/3)
  7. Calculus

    Given Z = 2(cos 148° + isin 148°) and W = 5(cos 11° + isin 11°), find and simplify z/w. 10(cos 137° – isin 137°) 0.4(cos 137° + isin 137°) 0.4(cos 137° – isin 137°) 10(cos 137° + isin 137°)
  8. Calculus

    The horizontal position of an object from a point of origin in meters is modeled by the function x(t)= (1+sin(t))/(2+cos(t)) where t is measured in minutes and 0 is less than or equal to t which is less than or equal to 5. A) show
  9. Trigonometry

    There are four complex fourth roots to the number 4−4√3i. These can be expressed in polar form as z1=r1(cosθ1+isinθ1) z2=r2(cosθ2+isinθ2) z3=r3(cosθ3+isinθ3) z4=r4(cosθ4+isinθ4),
  10. Calculus grade 12

    solve for (<_ = less than or equal to / pie = pie sign / -pie = negative pie) 3 sin²x = cos²x ; 0 <_ x < 2pie cos²x - sin²x = sinx ; -pie < x <_ pie

More Similar Questions