Juniven

 14 Find $\lim_{x \to 0} \frac{\ln (x^2+1)} {x^2}$ without L'hopital's rule 13 Finding plane equation given two lines 12 If $x^4+x^3+x^2+x+1=0$ then what is the value of $x^5$ 10 How can I prove this trigonometric equation with squares of sines? 9 Derivative of $f(x)=e^7+\ln(4)$.

### Reputation (8,814)

 +20 Show: $\cos \left( \frac{ 3\pi }{ 8 } \right) = \frac{1}{\sqrt{ 4 + 2 \sqrt{2} }}$ +10 Absolute value of a measurable function is measurable +10 Show that $|z - w| \geq \big||z|-|w|\big|$ +10 About the interior of the union of two sets

### Questions (80)

 13 About the interior of the union of two sets 6 Finding the value of $f'(0)$ 5 $\delta$-fined division and Lebesgue measure $\mu$ 5 About Lusin's condition (N) 4 Why is the Lebesgue Outer Measure of $\mathbb{R}$ equal to $+\infty?$

### Tags (125)

 118 calculus × 74 34 general-topology × 25 109 real-analysis × 69 33 integration × 31 81 limits × 41 30 algebra-precalculus × 14 57 sequences-and-series × 34 29 elementary-set-theory × 19 53 proof-verification × 33 28 derivatives × 17

### Bookmarks (505)

 1052 Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio? 756 The staircase paradox, or why $\pi\ne4$ 716 Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem) 664 What's an intuitive way to think about the determinant? 647 Does $\pi$ contain all possible number combinations?