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First step: n=1 we have 8¹ -1=7 which is divisible by 7. Assumption step: 8^k-1 is divisible by 7. Induction step: Using the previous step we have that 8^k-1=7x. So 8^k<...

Using the general rule d/dx(a*x^n) = a *n * x^(n-1) and the linearity of the derivative operator, we obtain:
6x^5+20x^3+0 = 6x^5+20x^3

(7 + √3)(7 - √3) = 7² + 7√3 - 7√3 - (√3)² = 49 - 3 = 46Alternatively you can go straight to identifying that this is the difference between two squares, using the fact that (a + b)(a...

Draw a diagram of the graph y=sin x between the stated interval. Identify the two extrema. Required interval is in between the two points.

A supremum is a number such that it is larger than all numbers in the given sequence. Although this is true for a maximum, the maximum has an additional property that it must be a member of the sequence s...