1. E

    Solve the limit problem

    How am I supposed to solve this problem??
  2. A

    Converting a limit into an integral.

    When we write $$ \lim_{n\to \infty} \sum_{I=1}^{n} f \left(a+ \frac{(b-a)}{n} i \right) \frac{(b-a)}{n} = \int_{a}^{b} f(x) dx $$ I really get a very big doubt about what is f(x). And most importantly what is $x$? Is $x$ the whole expression $\left(a+ \frac{(b-a)}{n}i\right)$ or $ i \rightarrow...
  3. A

    How to solve this example?

  4. idontknow

    Theory about limits

    Prove the following statements : After the limit turns to be an equation where L=pL or another transformation , then : For p>1 , L=\infty ; For p<1 L=0 Example: L=\lim_{n\rightarrow \infty} \dfrac{n^2 }{2^n }=\lim_{n\rightarrow \infty} \dfrac{n^2 +2n +1 }{2^{n+1} }=\dfrac{1}{2}L. Since...
  5. T

    Help with these limits!!

    a) lim x--> 0+ (sin (x))^x b) lim x-->infinity (pi/2 - arctan(x))^x
  6. A

    I need some resources for learning the evaluation of limits.

    The concepts of limits are quite clear to me, I did it from James Stewart Calculus and concepts are quite concrete too. But when it comes to evaluating the limits, I just can't figure out how to proceed, I mean there are some rules like we always try to do something so that zero doesn't ever...
  7. idontknow

    Limits with sequences

    Evaluate: a. l=\lim_{N\rightarrow \infty } \underbrace{sinsin...sin}_{N}N. b. l=\lim_{n\rightarrow \infty } n!^{-2n}\prod_{i=1}^{n}i^i . c. l=\lim_{n\rightarrow \infty } \frac{\sum_{i=1}^{n^2 }i^{-1}}{\ln(n)}.
  8. R

    Natural Logarithms with limits

    Hi, I am a bit confused about how to solve this equation below Limit x-->2 ln(x-1) _______ x-2
  9. B

    I can't understand how to prove limits using the definition...

    \lim_{x \to c} f(x) = L if \forall ε > 0, \exists δ>0 : 0 < |x-c| < δ => |f(x) - L| < ε , \forall x maybe except c. First of all do I understand what the definitions says? My understanding is this: "The closer x is at c the more precisely f(x) will approach L." In order to define this...
  10. C

    Multivariable calculus - Limits

    Show that the function f(x,y)=y/(x-y) for x→0, y→0, can take any limit. Construct the sequences { f(xn, yn } with (xn,yn)→(0, 0) in such way that the lim n→∞ f(xn,yn) is 3,2,1,0,−2. Hint: yn=kxn. I am not sure whether I am right, but I did the following: f(x,y) = kxn/(xn−kxn) =...
  11. T

    Evaluating limits algebraically

    Can anyone solve this, please? I'm stuck! \[\lim_{x \rightarrow 0}\frac{\frac{1}{\sqrt{9+x}}-\frac{1}{3}}{x}\]
  12. E

    Solving limits

    I asked some question about solving limits without derivatives and I solved this question using the method I learned from those questions I asked, but the sign of answer is different from what I have found can you please check my steps and see where I did wrong?
  13. E


    I can solve this question using derivatives but how can I solve it without using derivatives?
  14. I

    Solving a 3 variables equation, one happens to cause an oddity

    Hey, so we had this question in class: Given that the relationship between distance (m) and velocity (v) of an object is v^2 = 1 - m^3 Find the acceleration of the object when m=1 By taking the derivative of each side with respect to t 2v \frac{dv}{dt} =...
  15. R


    need these 2 solved lim x-->1 (-x^3 - x^2 - x - 1)= lim (-3x^2 + 4x - 2)= x-->00(infinity)
  16. I

    Questions about derivatives

    Hey. So we had this question: Given that f(x) = f(x+h) - 5x^3 h, find f'(x)? So our teacher solved it in two ways, one of them was this: f(x+h) - f(x) = 5x^3 h \large\lim\limits_{h \to 0} \large\frac{f(x+h) - f(x)}{h} = \large\lim\limits_{h \to 0} \large\frac{5x^3 h}{h} f'(x) =...
  17. R


    Hi I need to answer the following equation: \lim_{x\to2} (x³ + 3x - 1) = x3 = x to the power of 3
  18. L

    Multivariable Limits

    Has anybody idea on what techniques I can apply on these limits? at c and d I did direct substitution since there is no zero at the denominator. Is that correct? a) I converted polar form and denominator became cos^2Theta+Sin^2theta = 1 so that limit exists how about b? no techniques...
  19. W

    I want a deep understanding of Limits, Differentiation and integration

    Hello :) I'm a teacher in electronics department, I did a light basics of limits, differentiation and integration last semester in just solving problems. But I want a deep understanding of what these topics actually are? Where can I use limits? Is limits still valuable these days? What...
  20. A

    Optimization Problem with a decreasing constraint

    I need to find this maximum, $$ \max_{a\leq \frac{b}{1-db}}\frac{1}{1+da}(-a\log(a)-(1-a)\log(1-a)) $$ where $b\rightarrow 0$, $d=\frac{n}{b}$ and $n\in\mathbb{R}$ is a constant. ___________________________________________________________________________ Here is what I've done, first...