calculus

  1. Its possible integrate this with elementary calculus?

  2. Limit problem: $\lim_{t\to1} \frac {\sqrt {2t^2-1}\sqrt[3]{4t^3-3t}-1}{t^2-1}$
  3. Linear approximation to find worst case volume of a cone

  4. How to find the maximum surface area of a torus with a fixed volume?

  5. Show $f(x)=x\sec(x)$ is one-to-one on$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

  6. $L^1$ norm of derivative of Dirichlet kernel
  7. Show that $(ax^k+b)^{1/k}$ increases in function of $k$

  8. If we assume merely that the partials $D_jf$ exist in a neighborhood of $a$ and are continuous at $a$ then $f$ is differentiable in $a$.

  9. If (f ∘ f) is differentiable, is f also differentiable?

  10. convergent or divergent $\int_{-4}^{1} \frac{dz}{(z + 3)^3}$
  11. Solving the integral

  12. Show that the sequence $a_n = \frac{(n+1)^2 -n^2}{n}$ converges and give its limit.

  13. the infinite product bessel function product representation

  14. How to calculate integrals lilke $\int \frac{(2x+3)^C}{\sqrt x}dx$

  15. About a probability density function
  16. Examples of Axiom of Choice used in introductory-level undergradute math

  17. Determining the antiderivative of $\frac{1}{1+x^8}$

  18. How to compute the integral of $\int \sin(1-x^2)\,dx$

  19. Proving: If $|x-y|<\frac{1}{n}$ for every natural $n$ then $x=y$

  20. How to prove this equivalent

  21. Domain of this function:

  22. Linear approximation measure?

  23. Finding the general equation of a cross section of a roof and the position of each joist that makes up its surface

  24. Triple integrals with polar coordinates.

  25. How to prove that $\lim_{n\to\infty}\int_k^n\frac{\log_xn}{n\log x}\, dx=0$ for every $k\ge 2$

  26. Finding the mass of a body with changing density

  27. How to find real roots of an equation

  28. Shortcut to $x\uparrow \uparrow n$ for very large $n$ and $x\approx e^{(e^{-1})}$?

  29. Generalization of Liouville's theorem
  30. Summation of n terms of series using calculus

  31. What is the surface area of the plane $x+2y+2z=12$ cutoff by $x=0, y=0$ and $x^2+y^2=16$

  32. Inverse Laplace Transform of an exponential function 3
  33. Prove only by transformation that: $ \int_0^\infty \cos(x^2) dx = \int_0^\infty \sin(x^2) dx $

  34. Finding the domain of these functions:

  35. smallest constant $c$ for which: $|x^k - y^k| < c \cdot |x - y|$, with $x,y < 1/2$

  36. How to prove this inequality $f(a+b)\leq f(a) +f(b)$ for $\frac{f(x)}x$ monotone decreasing
  37. Finding the area swept out by a polar equation

  38. Increasing function g(x)

  39. Demonstrate $\frac{1}{2\pi} \int_{0}^{2\pi} cos^{2k}(\theta)d\theta = \frac{(2k)!}{2^{2k} (k!)^2}$ (problems with the hints)

  40. Evaluate the indefinite integral $\int\frac{(x(\pi + 49))^{\frac{15}{7}}}{\pi ^ {2} (x^{\pi}+7)} dx $

  41. If $f'(x_0)>0$, how do I explicitly show there is a neighborhood of $x_0$ in which the difference quotient is strictly positive?

  42. Evaluate the indefinite integral $\int\frac{((\arccos{(x)})(\sqrt{1-x^2}))^{-1}}{\ln{(1+\frac{\sin{(2x\sqrt{1-x^2})}}{\pi}})}dx$
  43. Maximum and minimum restricted
  44. Implication in the $(ε,δ)$-definition of limit
  45. Determining the range of $\varphi$ for a surface integral
  46. How do manipulations with differentials work? In particular, what does the following manipulation mean, and why is not valid?
  47. Solving the Differential equation: $y'=\frac{2}{x}y+x^3$
  48. Conditions for Inverse Function Theorem

  49. Maximize V/M of a cone

  50. Fourier transform of sigmoid function

  51. Prove: If $x_n=o(\alpha_n)$, then $x_n=O(\alpha_n)$. Show that the converse is not true.

  52. Is $h(x)=g(x) \circ f^{-1}(x)$ twice differentiable when $g$ and $f$ is?

  53. A function whose partial derivatives exist at a point but is not continuous
  54. Quicker way to prove convergence or divergence?

  55. $f$ is of $C^2$ therefore $g\circ f$ is of $C^2$, for all functions $g$?
  56. Let $f(x) = x^2$ if $x\in \mathbb{Q}$ and $f(x)=0$ if $ x\in \mathbb{R}-\mathbb{Q}$

  57. How to solve for maximum area of a rectangle under a curve?

  58. Find the area of the domain bounded by $ y^2-x^2+x^4=0$

  59. Differentiable functions using functions of functions

  60. Is the proof of $\lim_{\theta\to 0} \frac{\sin \theta}{\theta}=1$ in some high school textbooks circular?

  61. Functions not differentiable but continuous
  62. Define $f : \mathbb{R}\to \mathbb{R}$ by setting $f(0) = 0$, and $f(t)=t^2\sin(1/t) \text{ if } t\neq 0$

  63. Cylinder and sphere cuts

  64. Studying the function $f(x) = x^4-6x^2$ using derivatives: minima, maxima, inflection, concavity

  65. How many zeroes does the function $ f(x)=\exp(x)-3x^2$ have in $\mathbb{R}$?

  66. An approximation of the real part of $\int_0^{\pi/2}x\left(-1+\sin x\right)^{\log x} dx$

  67. integral by parts when term is squared

  68. Graph of continuous function from $[0,1]$ to $[0,1]$.
  69. Prove convergence / divergence of $\sum_{n=2}^\infty(-1)^n\frac {\sqrt n}{(-1)^n+\sqrt n}\sin\left(\frac {1}{\sqrt n}\right)$
  70. Discontinuous and Continuous Functions

  71. Find the area of the region enclosed by $x=2-y^2$ and $x+y=0$

  72. Finding: $\lim\limits_{x\to -\infty} \frac{6x^2+5\cos{\pi x}}{\sqrt{x^4+\sin{5\pi x}}}$

  73. Reference for Kalman-Ho-Narendra Theorem

  74. Total differential of weighted average

  75. How can I calculate $\lim_{x \to 0}\frac {\cos x- \sqrt {\cos 2x}×\sqrt[3] {\cos 3x}}{x^2}$ without L'Hôpital's rule?
  76. Volume of ball maximal in dimension 5

  77. What is the best way to learn Differential forms?
  78. Expansion of The Reciprocal of a Bessel Function
  79. optimization problem (window problem)

  80. Prove: $E=\{x\in \Bbb R^n |\sum_{i=1}^n|x_i|^p \leq1 \}$ is Jordan measurable.
  81. Find the length of the curve $y = 1/2 (x^2 / 2 - \ln x), \, 1 ≤ x ≤ e$

  82. An application of Young's inequality and without it.
  83. Convergence or divergence of $a_n=\frac{(n-1)!^2 \cdot x^{2n-2}}{(2n-2)!}$

  84. Brutal gaussian integral of death $\int_{\mathbb{R}} x \Phi(x) \phi(Bx-b)$
  85. Is it possible to calculate the direct limit by typing $ x = 0 $?
  86. Limit of sequence in which each term is defined by the average of preceding two terms

  87. Suppose we want to make $|x^2 \sin(1/x)| < \varepsilon$ where $\varepsilon > 1$, why does it not suffice that $|x| < \varepsilon$?
  88. Limit $\lim_{x \to \infty} \frac{x}{\log(x)}$.

  89. Some fundamental of limits
  90. Evaluating $\lim_{x \to 1^{-}} \prod_{n=0}^{\infty} \left(\frac{1+x^{n+1}}{1+x^n}\right)^{x^n}$
  91. Proving that: $f(t)\le \max\left(1,t/s\right)f(s)$ for concave function
  92. Convolution Integration
  93. help with polynomial to the $2$ power integration.
  94. What are the interior and acculumation points of given subsets of R
  95. Real roots of Irrational equation

  96. Convergence of series $(\frac{1}{3})^{2}+(\frac{1.2}{3.5})^{2}+(\frac{1.2.3}{3.5.7})^{2}+...$

  97. Evaluate limit of $\lim_{x \to \infty}\frac{x^x}{\left(x+2\right)^x}$
  98. Limit Inverse Trigonometric function

  99. A problem about Laplace transform and Parseval–Plancherel theorem

  100. Which of the following subsets of $\mathbb{R}^3$ constitute a subspace of $\mathbb{R}^3$?