Homework Statement
∫(2x+1)/(x²+2x+1)(x²+x+1)
Homework Equations
none
The Attempt at a Solution
I've foiled this out to look like:
∫(2x+1)/(x^4+3x³+4x²+3x+1)
I'm trying long division here but it's getting really ugly really fast. Should I foil this out in the first place or...
Homework Statement
for the following integrals, am I allowed to break them up like so:
1. ∫(1)/(sqrt(16-9x²)³) dx
= ∫(1)/(√16)³ · ∫(1)/(√-9x²)³ dx
2. ∫(x²)/(sqrt(x²-9)) dx
= ∫(x²)/(√x²) · ∫(x²)/(√-9) dx
3. ∫(1)/(x²(sqrt(a²+x²))) dx
= ∫(1)/(x²) · ∫(1)/(√a²) · ∫(1)/(√x²) dx...
Homework Statement
How do I know for sure when to use the power rule instead of the chain rule and vice versa?
Homework Equations
The Attempt at a Solution
Homework Statement
integrate:13((4^x)+(3^x))dx
Homework Equations
The Attempt at a Solution
I know the solution is 13((4^x)/ln(4) + (3^x)/ln(3)) + C
Can someone explain to me how this works? I don't know where the ln's are coming from. How would I differentiate this back to...
Homework Statement
derivative of: (14x^2)/sqrt(1-x)
Homework Equations
The Attempt at a Solution
I am at this point at finding the derivative:
(28x(sqrt(1-x))+((7x^2)/sqrt(1-x))/(1-x)
I am confused about the next step because don't know how it's derived from the previous...
Homework Statement
see title.
Homework Equations
no
The Attempt at a Solution
Ok so the solution is 16cos(2x) but I'm not sure how it is derived to that. I've tried the product rule but it's not working for me. What rule or rules do I use to get this solution?
Homework Statement
a) S(4 is higher limit, 0 is lower limit) (x^4 - x^2 + 1)dx
b) S(pi is higher limit, -pi is lower limit) (cosx + sinx)dx
Homework Equations
The S is the integration sign
The Attempt at a Solution
a) = ((x^5)/5)-((x^3)/3)+x I(4 high, 0 low)
=...
Homework Statement
S e^7x
Homework Equations
no
The Attempt at a Solution
Ok so I am using U-substitution for this problem but I don't know what to do next.
u = 7x, du = 7dx
How do I integrate e^u*du?
Homework Statement
a) S 13(4^x + 3^x)dx
b) S (cosx + sec^2x)dx
c) S (3-(1/x))dx
d) S e^(7x)dx
Homework Equations
The S is supposed to be the integration sign
The Attempt at a Solution
Are these correct or at least close?
a) = 13((4^x)/(ln(4) + (3^x)/(ln(3))) + C
b) =...
Homework Statement
a) d^2/(dx^2): ln(x+1)
b) d^3/(dx^3): x^7 + 4x^6 - x^2
c) d^2/(dx^2): 1/(x + 1)
d) d^4/(dx^4): cos(2x)
Homework Equations
none
The Attempt at a Solution
Can someone tell me if these are right?
a)= -(1/(x + 1)^2)
b)=210x^4 + 480x^3
c)= (2/(x + 1)^3)
d)=...
Homework Statement
What is the derivative of 14x^2?
Homework Equations
The Attempt at a Solution
Do i bring the 2 in front to get 28x? Or do I use the chain rule?
Homework Statement
I'm having trouble calculating these limits.
Homework Equations
none
The Attempt at a Solution
1. lim.......((lnx)^5)/(x)=
x->infinity
(((lnx)^5)/x)/(x/x)=
(((lnx)^5)/x)/1=
How do I calculate from here?
2.lim .......(14lnx^2)/(6lnx^3)=...
Homework Statement
lim (lnx)^2/x
x-->infinity
Homework Equations
none
The Attempt at a Solution
=5lnx/x * (1/lnx)/(1/lnx)
=5/(x/lnx)
How do I calculate x/lnx?
Homework Statement
Find intersection points of the following.(Conics are centered to origin)
Circle = x^2+y^2=4, Ellipse = (x^2/4)+(y^2/9) = 1
The Attempt at a Solution
So far I have this. (BTW I know the solutions are (-2,0) and (2,0) but I'm still unsure how to get there step...
Homework Statement
For each of the following functions, find a value of a, (if such a value exists), which makes the function continuous.
a) f(x) = {ax^2......x > 3
............{x - 7.......x ≤ 3
b) f(x) = {sin(ax)....x < (pi)
............{1............x ≥ (pi)
c) f(x) = {x^2 +...
Homework Statement
If f(x) < g(x) < h(x) for all x E R, and if f and h are continuous functions, must g also be continuous? If so, why? If not, can you come up with a counter example?
What do you think?
Homework Statement
Find the intersection points of: Line through (3,1) with slope -1/2, and ellipse through (-3,0) and (-2,2). No graphing just algebra.
The Attempt at a Solution
So far I have b=10/4 and a^2=9. I'm not sure how to finish this problem.
Homework Statement
Find the...
Homework Statement
Hello all, I am searching for help with conic intersections and i have a question I would like to ask.
-Consider the hyperbola x^2-y^2 = 1. A line in R^2 (All real numbers squared) can intersect this hyperbola in one of four ways: not at all, at one point crossing the...
Homework Statement
Determine what the tranformation does to the square with vertices (0,0), (0,1), (1,1) and (1,0). Draw the image of the square under these tranformations. Then find the change in area of the square under these transformations.
a)
[1 1]
[1 2]
b)
[0 -1]
[2...