(1) Suppose that (an)neN is a sequence of positive numbers that converges to a positive real number a. (a) Show that there exists an M such that an > for all n > M. (b) Prove that lim loge (an) = loge (a) using the definition of convergence. (You may use the inequality | loge (x) - loge(y)| ≤ for x, y > 0.) |x-y min{x,y}

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A: We have to find the value of x

A: The given quadratic equation is: x2-7x=-12

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A: 11+5x+2=33

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A: Use the exponent rules: 1). amn=am·n 2). If am=an then m=n.     (a). The given equation is:…

A: Given the equation  x5 + 17 = 35 We need to solve it. Now, x5 + 17 = 35 implies that  x5 = 35 - 17…

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