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 6 How to integrate $\int_{0}^{2\pi} \frac{1}{\sin^4x + \cos^4 x} \,dx$ 5 Proving that $\iint\frac{x-y}{(x+y)^3}\,dx\,dy$ does not exist over $0 \leq x \leq 1 , 0 \leq y \leq 1$ 4 Find coordinate points where the tangent line is horizontal for $f(x) = –\sin(8x) + 6\cos(4x) – 8x$ 4 Find the equation of a parabola with focal point $(-8, -2)$ and directrix $y -2 x + 9 = 0$ 4 Matrix complicated equation

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### Question (1)

 0 How to find the region of pre-images of a complex function?

### Tags (54)

 22 calculus × 14 7 derivatives × 5 21 multivariable-calculus × 21 7 algebra-precalculus × 4 13 integration × 7 6 analytic-geometry × 3 9 real-analysis × 5 6 matrices × 3 9 definite-integrals × 3 5 linear-algebra × 4

### Bookmarks (5)

 3 Manipulating tangent vectors 2 Let $f(x)$ be twice differentiable function, with $f(x) = x$ has $3$ roots 2 Principal part of Laurent series for $f(z)=\frac{1+z}{e^{z^2} - 1}$ at z=0 1 Verify Stokes' theorem by evaluating both the line and the surface integrals. 0 Original function when derivative has sharp turn