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Homework Statement Find a power series that represents $$ \frac{x}{(1+4x)^2}$$ Homework Equations $$ \sum c_n (x-a)^n $$ The Attempt at a Solution $$ \frac{x}{(1+4x)^2} = x* \frac{1}{(1+4x)^2} $$ since \frac{1}{1+4x}=\frac{d}{dx}\frac{1}{(1+4x)^2} $$ x*\frac{d}{dx}\frac{1}{(1+4x)^2}...

The series 0 + 3 + ... diverges. Since f(x) div, an also diverges. I get it how to use it now. Thanks!

ok so I get $$\lim_{t \to \infty} \int_0^t 3x dx = \lim_{t \to \infty} \frac{3}{2}x^2 |_0^t=lim_{t \to \infty} \bigg(\frac{3}{2}t^2 - \frac{3}{2}0^2\bigg)=\infty$$

I'm really confused about this test. Suppose we let f(n)=an and f(x) follows all the conditions. When you take the integral of f(x) and gives you some value. What are you supposed to conclude from this value?

Hi I'm reading a text about modular arithmetic, Prove that 16^43 - 10^26 actually is divisible by 21. They separate it by showing it is divisible by 7 and 3 they showed 16 \equiv 2 \textrm{ mod 7} \\ 16^2 \equiv 2^2 \equiv 4 \textrm{ mod 7} \\ 16 \equiv 2^3 \equiv 1 \textrm{ mod 7} \\ So...

AHHHH thank you!

From the text it says (P -> Q) or (P -> R) is equivalent to P -> (Q or R) I tried to see if this is true so I tried (P \to Q) \lor (P \to R) \\ (P \lor \neg Q) \lor (P \lor \neg R) \\ P \lor \neg Q \lor \neg R \\ P \lor \neg(Q \land R) \\ P \to (Q \land R) and P \to (Q \lor R) \\ P \lor...

Im just reading this one example and i am stumped at this one step. (R\to C) \land (S \to C) \\ (\neg R\lor C) \land (\neg S \lor C) \ \ \ \ \ \textrm{by conditional law}\\ (\neg R\land \neg S) \lor C \ \ \ \ \textrm{by distributive law} I don't understand how it went from the second step to...

So, intuitively no, since "i lifted my pen while drawing this function". I just googled the definition (i) the function f is defined at a Yes (ii) the limit of f as x approaches a from the right-hand and left-hand limits exist and are equal If a is the point that jumps, is the lim x-> a = 1...

Homework Statement Sketch the graph of a function f that is defined on [0,1] and meets the given conditions (if possible) - f is continuous on (0,1), takes on only two distinct values. Homework EquationsThe Attempt at a Solution...

Oh wow how did that happen! Thanks

Oh okay, it contains infinite planes! So I let the arbitrary vector (1, 1, 1) the I get - 2a+2b+2c=for some d. I just realize, how do I ensure this scalar equation is correct? Since I have points P and Q that needs to go through, it makes sense to sub abc with points P and Q. It seems I'm...

Thanks for the insightful question, I actually had to check my understanding. 3 points, anything less contains no planes? PQ cross with another vector gives me 1 plane. Since PQ cross another vector (x y z), this should give me any possible planes for some arbitrary vector, right?

Homework Statement Find the equation of all planes containing the points P(2, -1, 1) and Q(1, 0, 0) Homework EquationsThe Attempt at a Solution I use PQ to get a vector, (-1, -1, 1). I some how need to use another vector so I can use the cross product to find the planes. So i let another...

Homework Statement Does the line through the point P(1, 2, 3) with direction vector d = (1, 2, -3) lie in the plane 2x+y-z=3? Homework EquationsThe Attempt at a Solution From the 2x+y-z i can get the vector (2, 1, -3) and the direction vector, their dot product does not equal zero. So, no it...