jacky

### Questions (148)

 7 Find $\int^{\pi/2}_0 \frac{\sin^{n-2}(x)}{(1+\cos x)^n}\mathrm dx$ 7 Sum of square of binomial coeffcient with positive and negative terms 7 Finding $\int^{\infty}_{0}\frac{\ln^2(x)}{(1-x^2)^2} dx$ 6 series sum $\frac{1}{2}\cdot \frac{1}{2}k^2+\frac{1}{2}\cdot \frac{3}{4}\cdot k^4+\frac{1}{2}\cdot \frac{3}{4}\cdot \frac{5}{6}\cdot k^6+\cdots$ 6 Finding $\int\frac{\sin^4 x+\cos^4 x}{\sin^3 x+\cos^3 x}dx$

### Reputation (1,354)

 +5 maximum value of $\sum ab-2abc$ +5 probability of $3$ girls sitting together in back row of adjacent seat in vans -2 Evaluating $\int^{\infty}_{0}\frac{\cos x}{(x^2+1)^2}dx$ -2 Evaluate $\lim_{m\rightarrow \infty}\bigg[m^3\int^{2m}_{m}\frac{xdx}{x^5+1}\bigg]$

### Answers (26)

 8 Find $\lim\limits_{n\to\infty}\sum\limits_{k=1}^n \frac{2k+1}{k^2(k+1)^2}$ 3 Sum of cross terms vs sum of squares? 3 If $\displaystyle f(x) = \lim_{n \to \infty} ((\cos x )^n + (\sin x)^n))^{1/n}$. Then $_0 ^{\pi /2}\int f(x).dx$ is? 3 Number of real roots of equation $e^{\cos x} - e^{-\cos x} - 4 = 0$? 3 Computing the limit of the sequence $\lim_{n\rightarrow\infty}\overset n{\underset{k=1}{\sum(}}\sqrt{1+\frac k{n^2}}-1)$ and another one

### Tags (69)

 15 limits × 10 8 inequality × 17 12 calculus × 17 8 partial-fractions 12 limits-without-lhopital × 3 5 real-analysis × 6 11 sequences-and-series × 13 4 trigonometry × 29 8 integration × 18 4 definite-integrals × 12

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