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We know that f'(x) = x^3 + 2*x^0.5 + 8, and we can integrate both sides. This gives us f(x) = (1/4)*x^4 + (4/3)x^(3/2) + 8x + c, remembering to add the constant of integration. Now, we are almost...

= (4/3)x³ - (10/2)x² + x^1/2/(1/2) + C = (4/3)x³ - 5x² + 2x^1/2 + C

Let's look at what makes this question more difficult than, say, 0.5 or 0.01: as the decimal is recurring, you can't just multiply and divide by a big number to get a fraction. Example: multiply 0.01 time...

The idea here is to pair your numbers up to get to the solution. If you were to put this through a calculator it would take you a while. However, if we simplify the problem to the sum of 1 to 10 you'll be...

Key points: Approach in exactly the same way as if there was an = instead of an <.When trying to solve the inequality, remember that whatever you do to one side of the inequality you must also do to th...