# Holy cow

less info
reputation
115
bio website location age member for 6 months seen Dec 2 at 3:31 profile views 343

# 66 Questions

 4 If $f(x)$ is discontinuous at $x=0$, can $\int_{-1}^1 f(x)dx$ exist. 4 find the minimum value of $x^2-6x+9+ \dfrac{64}{x^2}$ 4 For $x>0$, Prove that $\dfrac{x}{1+x^2}<\tan^{-1}x < x$ 4 If $\lim\limits_{x \to \infty} f(x) = 1$, can we have function $f(x)$, such that $\int_0^{\infty}f(x)dx$ converges 3 Find $\int_0^2 \arctan(\pi x)-\arctan(x)\, \mathrm dx$ [duplicate]

# 98 Reputation

 +18 Find $\int_0^2 \arctan(\pi x)-\arctan(x)\, \mathrm dx$ -8 Find $\int_0^{2\sqrt{\pi}}\int_{x/2}^{\sqrt{\pi}}\sin(y^2)dydx$ +5 $f(x)=cx+\dfrac{1}{x^2+3}$. Find the values of c for which f(x) is increasing for all $x$ +5 Is the following series converging $\sum_{n=2}\dfrac{1}{(\ln n)^{\ln n}}$

 8 Find the sum of the series $\sum \limits_{n=3}^{\infty} \dfrac{1}{n^5-5n^3+4n}$ 2 Formula to estimate sum to nearly correct : $\sum_{n=1}^\infty\frac{(-1)^n}{n^3}$ 2 For $x>0$, Prove that $\dfrac{x}{1+x^2}<\tan^{-1}x < x$ 2 Prove that $s_n \leq 1+\ln n$, where $s_n$ is the $n$th partial sum of the harmonic series 1 Surface area of sphere $x^2 + y^2 + z^2 = a^2$ cut by cylinder $x^2 + y^2 = ay$, $a>0$

# 39 Tags

 15 calculus × 73 3 definite-integrals × 29 12 sequences-and-series × 18 2 harmonic-numbers × 2 8 algebra-precalculus × 12 1 multivariable-calculus × 23 8 summation × 8 1 polar-coordinates × 4 5 integration × 44 1 indefinite-integrals × 2

# 2 Accounts

 Mathematics 98 rep 115 Physics 1 rep