What is your difficulty with these? Several of these look like simple applications of basic rules. Why have you not made any attempt yourself?
Thanks you so much! Please attempt just a few if you don;t have much time.
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#1 A - Remember that the integral of a sum is the same as the sum of the integrals. Split the integral into two parts, evaluate each, and then find their sum.
B- For the second one, FOIL the terms and then evaluate as you did in the first problem. Remember to simplify all expressions after you square it.
#2 - Remember that (A+B)/C can be rewritten as A/C + B/C. Rewrite the integral as the sum of the two fractions and then evaluate each fraction.
#3 - Solve the function in terms of X. To find where it intersects with the y-axis, solve the equation for when y = 0. To find the gradient, find over which intervals the function is increasing by taking the derivative.
#4 - To find the tangent line, first, remember that the derivative of a function is the slope of the tangent line. So, find the derivative. Next, remember that y-y_1 = m(x-x_1) +b. We already have the given point, 0,0, so plug those coordinates in and evaluate y = mx +b. The m will be the derivative you found, and the b will be where the line intersects the y axis.
#5 - Solve y in terms of x and then plug in your value of y into the second equation, giving you only the variable x. Solve for x and then find y.
#6 - Factor the equation.
#7 - First evaluate the remainder from the first equation, and then divide x+1 into the second equation. The remainder should become obvious once you get to p.
#8 - If you deposit 2000 in and gain 4.5% every year, you're gaining a total of 1.045 every year. Over 20 years, that's 20*1.045 * 2000.
#9 - FOIL the equations out. This will give you x^4 - 8x^2 + 15. So, now when we put it back into the required form, we get (x^2 + a)^2 +b. Since a and b can be any constants, solve the quadratic to produce an 8x^2, and the constant term will be irrelevant. Thus, (x^2 -4)^2 will produce x^4 - 8x^2 +16. So, b must be -1.
I appreciate your help Math Major but i'm still havong trouble with a lot of the questions. I'm terrible at the basics of maths. I don't fully understand what i'm suppost to do when you say "evaluate" and "sum". I know the definitons but don't see what it is i'm supposed to do. It's really just the term i'm struggling with, I was taught pretty badly. What do you mean by "find over which intervals the function is increasing by taking the derivative.". For 6 do you mean just factorise it? That seems difficult. Last question what does "FOIL" mean?
Thanks for your time Math Major!
#3: Re-arrange to make y the subject. The gradient of the line will then be the coefficient of x. To find the y-intercept substitute x = 0 into the given equation and solve for x.
#6: It is is not hard to establish that roots of the quartic are x = 1 and x = -2. use the roots to construct factors. Divide the factors etc. All this stuff is in your class notes or textbook. You need to go back and look over it.
FOIL: Read this "FOIL": A Special (and Misleading) Case
You are strongly advised to go back to the algebra topics these questions cover and thoroughly revise them.
In future:
1. Please do not post so many questions in the one thread.
2. Please type the questions out rather than attaching them (it's not hard to do this and makes it much easier for people to read the thread and, perhaps, help you as well). People take time and effort to reply to these questions so it's only fair that posters take some time and effort to present their questions in a convenient way.
3. Please show what you've tried and say where you get stuck.