# rule

1. ### Trapezoidal rule with three subintervals

Common area between the circle x2+y2=4 and the ellipse x2+3y2=6 using Trapezoidal rule with three subintervals is: option given are: a)5.9268 b)8.5268 c)8.8420 d)9.5268 I am unable to solve this MCQ. Please someone guide me about how shall I proceed when it comes to deciding limits...
2. ### Chain rule

If, f(x+2)=e^(x)*g(x^(2)+1) and g(1)=5 are given find f'(2)? Can you explain this step by step cause I have problem understanding chain rule
3. ### Sine Rule: Can this be solved?

Sorry for the bother... Yeah, it is an elliptical problem. I know I am missing data to complete the use of the Sine Rule to solve it, but I am just wondering if knowing that C+A is already a known value might help. Just I cannot see it. There are other ways to solve it, I know, but I wanted...
4. ### Divisibility rule

If 3 divides n for n \in N Show that the sum of digits of n must be divisible by 3
5. ### Descartes Rule not verifying

The roots are -1, -2, 5, i, -i for: P(x)= x^5-2X^4-12x^3-12x^2-13x-10 using Descartes Rule to verify: The rule says the number of positive real zeros of P(x) is the same as the number of sign changes in the sign of the coefficients or is less than this by an even number.. I see only one...
6. ### Calculus - Chain Rule

Let f1(x) = e^x, f2(x) = e^f1(x) and generally fn+1(x) = e^fn(x) for all n . For any fixed n, Find the the derivative of fn(x) Please help
7. ### Chain rule

Car A is traveling north on Highway 152 and car B is traveling west on Highway 251. Each car is approaching the intersection of these two highways. At a certain moment, car A is 0.7 km from the intersection and traveling 95 km/h while car B is 0.7 km from the intersection and traveling at 80...
8. ### Descarte's rule of signs proof

Prove by induction on n that if p(x) is a polynomial of degree n then the function $e^{x}-p(x)$ has at least n+1 zeros. By zero I mean that f(x) for some x=0 This is my solution however I feel the proof is incomplete and missing some theorems. https://imgur.com/a/gY92N
9. ### Use 0 in rule of 3?

Hello! I'm doing a AHK script. If 0 does nothing, 1 doubles, what do I do with this: (16/9)/0=(14/9)/x? The number 0 in rule of three screws it all. I just want to have 0 as a normal number. I tried changing 0 to 1 and then subtract 1 from x. It gave me -0,125. I don't know if it worked or if...
10. ### Derivatives: Chain Rule - Marginal Revenue Product

I am having trouble with part c of this question. I have already solved A and B but if someone could help me with part c I would greatly appreciate it. A factory owner who employs m workers finds they produce q=1.2m(1.2m+46)^3/2 units of product per day The total revenue R in dollars is R=...
11. ### How to see when to use which rule?

I managed to get through this exercise, because I knew the answer, and I knew that I had to use the chain rule ( ? ) But I still have trouble understanding, how can I know which formula to use? You can take this exercise as an example. Could someone explain, why I had to use the chain rule?
12. ### finding limit((exp(-sin(x))-1)/(x),x,0) without L'HÃ´pital's rule?

Hi Guys Can you help me with this problem? limit((exp(-sin(x))-1)/(x),x,0) I want to know how to solve this without L'Hospital's rule.. thank you :))
13. ### Chain rule concept question

Hello all, I have a quick question on the chain rule for derivatives. I have used it hundreds of times through out my study of calculus, but embarrassingly I get a little confused when, for example, you're doing a related rates problem and you take the derivative of a function you developed...
14. ### using chain rule for finding dg(x)/dx given f(g(x)) and df(x)/dx

I have a problem that says: f(x) and g(x) are differentiable, given that f(g(x))=x and df(x)/dx = 1+[f(x)]^2 show that dg(x)/dx= 1/(1+x^2)! Am I correct to say since f(g(x))=x, then df(x)/dg(x)=1 ? then I wrote df(x)/dx = 1+[f(x)]^2= df(x)/dg(x) * dg(x)/dx =dg(x)/dx! I don't know what...
15. ### help with finding limit without using L' HÃ´pital's Rule

Hello everybody I appreciate your help with this problem: limit (((1+tan(x))^0.5-(1+sin(x))^0.5)/x^3,x->0) I can solve this with L' HÃ´pital's Rule by differentiating the numerator and denominator 3 times and finding the limit of the resultant numerator and denominator when x->0 and...
16. ### Derivatives: Chain Rule - Marginal Revenue Product

All answers involve a unit of dollars, so you must enter your answers accurate to two decimal places! A factory owner who employs m workers finds that they produce q = 1.8m(1.8m+18)^3/2 units of product per day. The total revenue R in dollars is R=1544q / (344448+4q)^1/2 (a)...
17. ### Chain Rule

Solved it. The end.
18. ### Sigma rule question

Hi everyone I was wondering why this equality is true considering that $d_i$ is not a constant $\sum E(d_{i}u_{i})=\sum d_{i}E(u_{i})$ $$d_{i}=(x_{i}-\bar{x})$$ Thank you in advance
19. ### Chain Rule?

I'm trying to learn this stuff by myself. Can someone explain to me how to find the derivative of "sin(sin(sin(sin(sin(x)))))" using the Chain Rule? I'm confused by the whole concept. Thank you.
20. ### Multivariable Chain rule proof : is it correct?

Hello, I've had a go at proving the chain rule for a composition that maps from R^2 to R to R. There are two images attached. I've used the "arithmetic of limits" rules throughout, that if two limits exist, their product limit and sum limit exist etc. Any thoughts / scrutiny would be...