### Questions (46)

 6 convergent or divergent $\int_{-4}^{1} \frac{dz}{(z + 3)^3}$ 6 Find n so that the following converges $\int_1^{+ \infty} \left( \frac{nx^2}{x^3 + 1} - \frac 1 {13x + 1} \right) dx$ 4 Estimate the error that results when $\sqrt{1 + x}$ is replaced by $1 + \frac{1}{2}x$ if $|x| < 0.01$ 3 How to change the value of $a$ in a Taylor series yet still get the correct approximation? 3 Prove $\lim_{x \to 1} \frac{x^b - 1}{x - 1} = b$

### Reputation (442)

 +5 Basic property of kronecker delta $( A \otimes B)(A^{-1} \otimes B^{-1})$ +8 Example of KKT conditions using single variable, how to set up +3 Optimization, Are all points feasible if there is only one constraint? +5 Optimisation - first order necessary conditions, directions, Chong & Zak Q. 6.16

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### Tags (68)

 0 calculus × 11 0 linear-algebra × 5 0 real-analysis × 9 0 integration × 5 0 optimization × 9 0 simplex × 3 0 convex-optimization × 7 0 lagrange-multiplier × 3 0 multivariable-calculus × 5 0 limits × 3