Can someone help me with math? Just started doing derivatives and I only know the basic rules (sum/difference of derivatives, product, quotient rule, I don't know chain rule) and I can't seem to get the right answer to this question. Can anyone point me where I'm wrong? f(x) = [3(1 - sin(x))] / (2cos(x)) (Distributed the 3 over the (1 - sin(x)) > (3 - 3sin(x)) / (2cos(x)) (Rewrote the function as two fractions) > (3/2)(1/cos(x)) - (3/2)(sin(x)/cos(x)) (Trig identities) > (3/2)(sec(x)) - (3/2)(tan(x)) (Differentiated here. 3/2 is a constant multiple so I just multiply it with the separate derivatives. I know that d/dx (sec(x)) = sec(x)tan(x) and d/dx (tan(x)) = sec^2(x). Since this is just a difference of two terms, I can just subtr
Who is the smartest person in all of history? I'm writing for a topic in psychology and it has to do with intelligence. I'd like to incorporate different types of intelligence, and so I thought it'd be helpful to ask a varied array of people for their opinion on who is the smartest person (famous) they know, because I'm assuming different people will consider intelligence from different perspectives. So Basil, in your opinion, who is the smartest person that has ever lived?
Could someone help me with math? Sequences and series I've got a question that I'd appreciate if anyone could tell me where I'm going wrong with this... How many terms, n, must be added in an arithmetic sequence whose first term, a_1, is 11 and whose common difference, d, is 3 to obtain a sum of 1092? This is what I'm doing: > 1092 = 11 + 14 + 17 + ... + a_n [Set up the series] > 1092 = (n/2)(2*a_1 + d(n-1)) [The formula for the arithmetic series is (n/2)(a_1 + a_n). However, a_n can be rewritten as the sum of (a_1 + d(n-1))] > 1092 = (n/2)[2(11) + (3)(n-1)) [Plugged in the values given] > 1092 = (n/2)(3n + 19) [Simplified inside parenthesis) > (2)1092 = 3n^2 + 19n [Carried out the multiplication involved in (n/2)] ...and thi
Need help with math I missed class the other day and my textbook is as clear as mud. I'm in Calc 2 and the section's about power series I'm being asked to find the values of x for which f(x), f'(x), and integral of f(x) each converge. I've figured out how to find convergence by myself but I don't understand how to differentiate or integrate a power series. For example, if I have f(x) = sigma [((-1)^(n+1))((x-1)^(n+1))]/(n+1) how do I differentiate or integrate this thing?
Need help with math I missed class the other day and my textbook is as clear as mud. I'm in Calc 2 and the section's about power series I'm being asked to find the values of x for which f(x), f'(x), and integral of f(x) each converge. I've figured out how to find convergence by myself but I don't understand how to differentiate or integrate a power series. For example, if I have f(x) = sigma [((-1)^(n+1))((x-1)^(n+1))]/(n+1) how do I differentiate or integrate this thing?
Need help with math Not asking for a step-by-step process of how to do this, but does anyone know how to approach this integral? ∫ 1/[sq.rt(x)*(x +6)] dx I have no idea how to integrate it. After putting it in wolframalpha, all I could think of would be that integrating it involves trig substitution, but I gave it a shot and it seemed like hell trying to simplify what came out. The only other thing that comes to mind is partial fractions, but I can only do that with linear factors and irreducible quadratics.
Need help with math Don't know what I'm doing wrong here... lim (x -> 0+) x^(1/x) y = lim (x -> 0+) x^(1/x) ln(y) = lim (x -> 0+) (1/x)ln(x) ln(y) = lim (x -> 0+) ln(x)/x As x approaches 0 from the right, the numerator approaches -∞ and the denominator approaches 0... this gives the form of (-∞/0) Applying L'Hopital's Rule: ln(y) = lim (x -> 0+) 1/x As x approaches 0, the expression approaches ∞, so: ln(y) = ∞ e^∞ = y y = ∞ But this is wrong. What am I doing wrong?
Need help with Limits I don't need any help with actually solving anything, but I need something clarified... In lim (x ->pi/2) cos(x)/cot(x) why can't I use direct substitution to find the limit? My teacher told me that I can use direct substitution for polynomial, rational, trig, and log/exp functions when direct substitution doesn't yield undefined values since those functions are continuous on those intervals. Yet, if I directly input cos(pi/2) / cot(pi/2) > (0/1) / (0/1) = 0, which is incorrect. Why is this? Neither cosine pi/2 or cotangent of pi/2 are undefined.
Need help with Limits I don't need any help with actually solving anything, but I need something clarified... In lim (x ->pi/2) cos(x)/cot(x) why can't I use direct substitution to find the limit? My teacher told me that I can use direct substitution for polynomial, rational, trig, and log/exp functions when direct substitution doesn't yield undefined values since those functions are continuous on those intervals. Yet, if I directly input cos(pi/2) / cot(pi/2) > (0/1) / (0/1) = 0, which is incorrect. Why is this? Neither cosine pi/2 or cotangent of pi/2 are undefined.
Need help with math Last problem on the set of problems I Have to do and my mind is exploded and i've confused myself... Anyone know how to do this? Find the area enclosed by an ellipse with the formula (x^2/a^2) + (y^2/b^2) = 1 and where the upper half can be described with y = (b/a)sq.rt(a^2 - x^2) and the lower half with the same thing but with a negative... (-a, 0), (a,0) and (0,b) are points on the graph. That's all i'm given. Graph is kinda like this:
Can someone help me with math? I've just learned about the Chain Rule and I've been finding derivatives without too much of a problem, but I've come to a bind here and I don't understand what I'm doing wrong. "Differentiate y = sq.rt(x) + 1/4[sin(2x)^2]" The equation is a sum, so you can just take the derivative of both components of the sum separately. The derivative of sq.rt(x) is 1/2sq.rt(x). I have to use the Chain Rule for the last component. I like to work out and then go in, so this is what I did: y' = 1/2*sq.rt(2) + 1/4(cos(2x)^2)) * d/dx (2x)^2 I took the derivative of sine since it's the outermost function. The derivative of (2x)^2 is 4x. This gives me: y' = 1/2*sq.rt(2) + 1/4(cos(2x)^2)) * 4x y' = 1/2*sq.rt(2) + x(cos(2
what am I doing wrong? math I'm doing integration techniques and I don't know what I'm doing wrong here... ∫arcsec(2x) dx (x > 1/2) Let u = arcsec(2x), du = 2/x*sq.rt(x^2 - 1), dv = dx, v = x ∫arcsec(2x) = xarcsec(2x) - 2∫1/sq.rt(x^2 - 1) dx I cancelled the x's (x in the denominator of du is just x since x is always a positive value) Now, using (x^2 - 1) with reference to a right triangle, x is the hypotenuse, and the measurement of the legs are 1 and sq.rt(x^2 - 1). I decided to use 1 as the bottom leg and sq.rt(x^2 - 1) as the right leg where theta is an acute positive angle. tan(θ) = sq.rt(x^2 - 1) sec(θ) = x which means sec(θ)tan(θ) dθ = dx Rewrote integral as ∫arcsec(2x) = xarcsec(2x) - 2∫(sec
Chemistry Help EDIT: Nevermind I've got it figured out. Thanks.
Basilers who work out, are pre workouts worth it? I see a lot of my friends talk about hyde and it seems like they can't workout without it. I'm thinking of trying one out but I'm scared the same thing will happen to me. Is there a lighter pre workout I can try to see how well I gauge this stuff? I heard about jack3d and was thinking of that but people tell me that it's not any good now and it doesn't do anything.
Is my crackpot conspiracy theorist friend right? My friend says that drinking fluoridated water will mess up your brain. He says that it makes perfect sense because that way the government will be able to "control the masses". I got curious and searched around for a credible source, but couldn't find anything, which was a little surprising considering that it's a popular idea which has been floating around for quite a while now. Does anyone on here know of a good credible source that has dealt with this?
I need help with Math I really just haven't done trig in a while, so I'm a little rusty... I'm supposed to find the absolute extrema of y = (e^x)(sin(x)) in the interval Extrema may occur in endpoints and at places where derivative is either zero or undefined, so I took the derivative y' = (e^x(cos(x)) + e^x(sin(x))) Factored y' = e^x (cos(x) + sin(x)) This equation can never be undefined, and by looking at the separate factors, e^x can never be equal to 0 ...but like I said, I haven't done trig in a while and I forgot what to do for cos(x) + sin(x) = 0 What do I do?