9 Evaluate $\lim\limits_{n \to \infty}\left(\frac{1}{1+a_1}+\frac{1}{1+a_2}+\cdots+\frac{1}{1+a_n}\right).$ 7 Solving $9^{1+\log x} - 3^{1+\log x} - 210 = 0$ where base of log is $3$ for $x$ 6 calculating the arc length of a function 6 If $Y\sim\operatorname{Beta}(a,1-a)$ and $Z\sim\operatorname{Exp}(1)$, then $YZ\sim\operatorname{Gamma}(0,1)$? 5 How would I algebraically determine if a triangle whose vertices A(2,6) B(9,0) C(3,6) is a right angle triangle?

### Reputation (3,139)

 +10 If $\lim_{x\to 1} \frac{f(x)-6}{x-1} = 10$, then what is $\lim_{x\to 1} f(x)$? -2 In determining probability using 2 dice rolls why are permutations (x,x) not counted twice? +10 Solve the equation for x: +15 Is the squeeze theorem still valid when $|b_n| \leq |c_n| \leq |a_n|$?

### Questions (5)

 1 $\lim \limits_{n\to\infty} \sum_{k=1}^{n} \frac{1}{ka+n}$ 1 Expected Waiting Time in a Queue with exponential distribution 0 Difference of dependent Chi-squared distributions 0 Correlation between Least Square Parameters obtained in Linear Regression -1 Evaluate symbolic expression in MATLAB

### Tags (103)

 30 calculus × 25 19 real-analysis × 14 27 probability × 33 18 logarithms × 6 26 integration × 17 13 probability-distributions × 11 20 limits × 13 13 sequences-and-series × 4 20 trigonometry × 9 11 substitution × 3

### Bookmarks (6)

 665 What was the first bit of mathematics that made you realize that math is beautiful? (For children's book) [closed] 121 List of interesting math podcasts? 4 How many solutions are there to $x_{1} + x_{2} + x_{3} + x_{4} = 15$ 2 Flip a biased coin and win/lose money 2 Find $\lim_{n \rightarrow \infty} P(n[Y_n]=k)$