Huang
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306
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 4 Finding all functions $f$ satisfying $f'(t)=f(t)+\int_a^bf(t)dt$ 2 Prove that the equation $x^{10000} + x^{100} - 1 = 0$ has a solution with $0 < x < 1$ 1 how to find center of an arc given start point, end point, radius, and arc direction? 1 Any idea how to solve this equation? 1 Integral of product of two functions in terms of the integral of the other function

### Reputation (306)

 +10 Prove that the equation $x^{10000} + x^{100} - 1 = 0$ has a solution with $0 < x < 1$ -2 IF $f(x) = \int_{0}^{\phi (x)} g(t) dt$, How could we find $f'(x)$? +15 Any idea how to solve this equation? +2 Why is arctan of $-\frac{\sqrt{3}}{3} = -\frac{1}{6}\pi$?

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### Tags (9)

 5 logarithms × 2 2 polynomials 4 calculus × 3 1 algebra-precalculus 4 differential-equations 1 geometry 4 integral-equations 1 circle 3 real-analysis × 2

### Accounts (4)

 Chinese Language 7,568 rep 1834 Stack Overflow 3,410 rep 21117 Mathematics 306 rep 15 Area 51 201 rep 2