# calculus

1. ### Some limits manipulation.

Could someone explain the steps involved in this limit? I'm reading a proof and kinda stuck here. For k \in \mathbb{Z}^+ and c a positive constant, set \beta_k = c \sqrt{\frac{k}{\ln(k)}} and \delta_k = \frac{\ln(\frac{k}{\beta_k})}{k}. Then \lim\limits_{k \to \infty} (\beta_k(1-\delta_k)^k +...

The question is in the picture.
3. ### Differentiating the equation of curvature equation

Hi everyone, The equation for the curvature(k) is the following: (1) k = (y'')/((1+(y')^2)^3/2) For small deflections, this is just simplified to y'' (the numerator) In beam theory the following equation is used: (2) EIy'' + Py = 0, where the y'' is referring to the simplified curvature...
4. ### I require a hint in solving this indefinite integral.

The problem I want to solve is this \int\frac{ (\sin^n \theta - \sin\theta)^{1/n} \cos\theta}{\sin^{n+1}\theta} d\theta Now, if I make a substitution of u = \sin\theta then, the integral would look like this \int \frac{(u^n -u)^{1/n}}{u^{n+1}}du . No matter what substitution I make the...
5. ### How I solve this Integral by Residue Theorem?

Solve the Integral with Residue Theorem.
6. ### Does the Finite Calculus exist?

Does the Calculus of Finite Differences exist as an extended field of Advanced Mathematics? (Please, don't confuse it for Discrete Mathematics.) Is it the synonym of the Discrete Calculus? Is it applicable for Pure & Applied Physics nowadays? Could you recommend some resources for such subject?
7. ### Inequality #2 without calculus

Given x^y < y^x , where x>y \geq \lambda >0, find the range of \lambda . Without calculus!
8. ### Prove inequality without calculus

Prove that a^b < b^a , for a>b\geq 3.
9. ### Comparing large numbers without calculus

A curious logical consequence of the principle of non-contradiction is that a contradiction implies any statement; if a contradiction is accepted as true, any proposition (or its negation) can be proved from it. Let's try (*)66^{77} > 77^{66} . I will prove (*) using sgn function(analytic...
10. ### Help with Calculus II Problem

Need help with this one. Can't seem to solve it. Thanks in advance
11. ### Calculus

Find the area of the region bounded above by y=x, and bounded below by y=x^2 and bounded on the sides by x=0 and x=1. HELP PLEASE!
12. ### Which of the following statements is correct ?

This is a question from a college admission exam. There is a mistake in the attachment. f is derivative not differentiable.
13. ### Why radians and not degrees in calculus?

I know it's stating the obvious elephant in the room when it comes to calculus and that you should always use radian measure anytime you use trig'; I've just always accepted it as a rule. But I've never once witnessed someone give a sound geometrical argument why this is so. Could someone give...
14. ### Academic Guidance I need some advice for a preparation for an exam.

Hello! Recently, I discovered about a good scholarship. I decided to apply but there's a tough exam to pass in order to get the scholarship. The most of the questions are focused in those topics: Algebra:Functions, Polynomials, Inequalities Pre-calculus/Some years have calc1~3 questions. Real...
15. ### Inequality with integrals

Let "k" be a constant on [1/4;1]. Prove that exists:
16. ### Multivariable calculus

I am unable to set the limits and reach the conclusive answer and mark the correct option. I am trying to put the the solution in cylindrical coordinates but the answer I am getting is not matching with the options. Please help with the answer and more important the steps to reach such a...
17. ### Multivariable calculus - Limits

Show that the function f(x,y)=y/(x-y) for xâ†’0, yâ†’0, can take any limit. Construct the sequences { f(xn, yn } with (xn,yn)â†’(0, 0) in such way that the lim nâ†’âˆž f(xn,yn) is 3,2,1,0,âˆ’2. Hint: yn=kxn. I am not sure whether I am right, but I did the following: f(x,y) = kxn/(xnâˆ’kxn) =...
18. ### Help Needed please I don't know where to start from.

The question is. Consider the function f(x)=sqrt(x)/sin(x),0<x<pi Show that the x coordinate of the minimum point on the curve y=f(x) satisfies the equation tan x=2x the question is worth 5 marks/points