Find the natural domain
Course:- Mathematics
Reference No.:- EM13470

Assignment Help
Assignment Help >> Mathematics

1.  Find the natural domain of the following functions. Explain your results.

466_Mathematics problems.png

2. Given the equation y= x2 - 6x +8, find the following:

     (i) For what values of x is y  = - 10?
     (ii) For what values of x is y = ≥ 0 ?
     (iii) Find the minimum value of y.
     (iv) Find the maximum value of y.
3.  (a)Sketch the graph of y = x-1/x by translating, reflecting, compressing and stretching the graph of y =1/x

     (b) Find an expression for f o g, given that:

2017_Mathematics problems1.png

 4. Find the equation of all lines passing through the point (6, -1) for which the product of  their x- and y- intercepts is 3. Sketch these lines.

5. (a) Find the amplitude and period, and sketch at least two periods of the following function: 

       y = 1/2 cos(3x - Π)

      (b)  Express the following expression as a single logarithm:                        

          2ln(x+1) + 1/3 ln(x - cosx)
6. Find the expression for:  (i)  ) sin(cos-1x ) and  (ii) tan(cos-1x).


7. Solve the following equation for x:

567_Mathematics problems2.png

8. Find the limit of the following:

2232_Mathematics problems3.png

9. Find :

1482_Mathematics problems6.png


10. Find

735_Mathematics problems5.png

Put your comment

Ask Question & Get Answers from Experts
Browse some more (Mathematics) Materials
A company wishes to manufacture a box with a volume of 36 square feet that is open on the top and is twice as long as it is wide. Find the dimensions of the box produced fro
Determine the largest domain Ω on which the function f(z) = log z / z is analytic, where log z is the principal branch of the logarithm. Furthermore, compute f'(z) on your d
To determine the number of deer in a preserve, a conservationist catches 468 deer and tags them then lets them loose. Later, 680 deer are caught, 170 of them are tagged. How
If a quadratic function can be used as a model, we can find such maximums or minimums by finding coordinates of the vertex. EXAMPLE 1 Fenced-In Land. A farmer has 64 yd of f
Compute the probability that a permutation of n objects is a derangement for all positive integers not exceeding 20 and determine how quickly these probabilities approach th
F(t) = A + B cos (ω (t-Φ)) where A, B, ω, and Φ (with 0 ≤ Φ ≤ 28 ) are constants and t is in days. Use the data above to find the four parameters. If ovulation occurs around d
In Aaliyah's grade, 2/3 of the students have a sister. Of the students who have a sister, 1/2 also have a brother. What fraction of the students in Aaliyah's grade have bo
Find the midpoint and length of the line segment PQ where P=(2,-7) and Q=(5,1). We will also use vectors to find the length of the segment.