# rule

1. ### L'Hopital's Rule on an Absolute Value function. Two different answers?

Suppose there is a function, k, which is equal to . Now suppose I take the limit as n approaches infinity, so that . Now, I am at a crossroads. Do I: A)keep the absolute value bars and simply evaluate the limit of the function inside them? Or; B)remove the absolute values since we know...
2. ### Find the Derivative

I have two questions. They are almost similar. I wanna know if their derivative will be same or different. (a) If y = u^5 - 8u^2 + 2u - 1, and u = (x + 10)^(1/2), find dy/dx when x = -9. (b) If y = u^5 - 8u^2 + 2u - 1, and u = (x + 10)^(1/2), find dy/dx.
3. ### need help with L'Hôpital's rule

hi every 1! im need ur help with this exercise. full solution will help.
4. ### L'Hopital's Rule

Find the limit of x^(1/x) as x approaches 0 from the right. I keep getting positive infinity as the answer. The textbook shows zero to be the answer. Can someone help me?
5. ### Generalized Power Rule with Products and Quotients

Just wanted to make sure I'm doing this correctly: y = 5(x + 3)^2(2x - 1)^5 y' = 5(x + 3)^2[5(2x - 1)^4*2] + (2x - 1)^5[10(x + 3)*1] ----- y = (2x - 7)^2 / (4x - 1) y' = {(4x - 1)[2(2x - 7)*2] - (4)(2x - 7)^2} / (4x - 1)^2 This is as far as my professor requires me to go; no combining...
6. ### HELP!!!! Formal proof of validity using rule of replacement or ACP or UI|EG|UG|EI

discrete assignment, need help asap! Deadline: Tomorrow
7. ### L'Hopital's Rule and a trig function - I still get limit of 0

Hi, I am trying to find the lim(x-o) tanx^2/x^2 Using L'Hopital's Rules I differentiated the numerator and denominator separately giving: limx-0 = 2xsec^2(x^2)/2x If I put zero into that equation don't I still get 0? I also tried: limx-2 = 3 x^2-x-6/x-3 and got: 2x-1 which I think is...
8. ### Differentiating fractions without the quotient rule?

Differentiate y=\frac{x^{2}}{(x+4)} without using the quotient rule. Can you use the product rule to differentiate above? If so, what are the steps? y=x^{2}(x+4)^{-1} \frac{dy}{dx} = 2x(x+4)^{-1}+x^{2}(1)^{-1} Is the above correct so far? If not, where did I make the mistake? :)
9. ### Find limit without LHospital's rule

\lim_{x\to\ \pi/4} \frac{1-\tan x}{1-\sqrt{2} \sin x } How do I find the limit without using L'Hospital's rule ?
10. ### rule of life

hello,good morning how are you.i am bandana thakur A Rule of Life helps us to live a Christian life more intentionally. Father Brown (2013) Season 4 Episode 6 live stream Benidorm Season 8 Episode 1 live stream Silent Witness Season 19 Episode 3 live stream Adventure Time Season 7 Episode 17...
11. ### rule of life

hello,good morning how are you.i am bandana thakur A Rule of Life helps us to live a Christian life more intentionally. Father Brown (2013) Season 4 Episode 6 live stream Benidorm Season 8 Episode 1 live stream Silent Witness Season 19 Episode 3 live stream Adventure Time Season 7 Episode 17...
12. ### L'Hospital Rule

Hello! I encountered the following limit and I can't seem to find the trick to solving it: \lim_{x \to 0^+} x^{-1}ln(x) First of all, we need to manipulate the function to give us an indeterminant form of 0/0 of inf/inf. I tried: f(x)= \frac{x^{-1}}{ 1 / ln(x)} , but after applying...
13. ### sine rule and where is hypotenuse.

They teach sine rule with non right-angle triangle. How do you find sine in a triangle that does not have hypotenuse. https://www.youtube.com/watch?v=RL2F49BwQTA
14. ### Decartes' Rule of sign.

x^5-7x^4+15x^3-5x^2-16x+12 Positive: 4 or 2 Negative: 3 or 1 Positive:4,2,2 Negative:1,3,1 Imaginary:0,0,2 Did I do this right?
15. ### Partial derivative chain rule problem.

So far this is what I get. However my answer is not correct. Could someone please help me find out why? Thanks! $x=e^{3s}cos(5t)$ $y=e^{3s}sin(5t)$ \$\frac{\partial u}{\partial s}=\frac{\partial u}{\partial x}\frac{\partial x}{\partial s}+\frac{\partial u}{\partial y}\frac{\partial y}{\partial...
16. ### Determine if sequence converges or diverges using l'Hopital's Rule

Can we use l'Hopital's Rule as another alternative in solving this problem like how I showed in my work?
17. ### Chain rule partial derivative

Using the chain rule, dv/dt=dv/dx*dx/dt+dv/dy*dy/dt dx/dt=-4t -> evaluate at (1,1) =-4 dv/dt=-4dv/dx+4(-2) dv/dt=-4dv/dx-8 How can I find the missing dv/dx in order to get a value for dv/dt? Thanks!
18. ### Independence and Multiplication rule help

Hi guys, I'm back again with another question hopefully you guys can help me. [Question] We have a fuse box with 20 fuses, 5 of which are defective. If 2 fuses are selected at random, in succession, and without replacement, what is the probability that both fuses are defective? [SOLN] A =...
19. ### formula for l hopital rule

i have question for no 3 , why the e ^ ln y = e^lim( g(x) f (x) ) , why not e ^ lim ln y = e^ lim( g(x) f (x) ) ?
20. ### limit of (x)^(1/x) as x approaches infinity using l hopital rule

limit of (sqrt rt (x^2 + x)- x ) as x approaches infinity using l hopital rule i managed to gt sqrt rt ( ∞² +∞)-∞ , which is also equal to ∞ , but the ans given is 0.5 , how to do that ?