Question 6 A piecewise function f is defined below. √x+cxx<10 f(x) = cr²-5z r>10 Let's find the value of c that will ensure f is continuous on (-∞0,00). Since each piece of f is a polynomial, we know that f is continuous over each piece of its domain. In other words, f is continuous on (-∞0, 10) U (10,00). For f to be continuous on (-∞0,00), we need to ensure f is continuous at z = 10. So we start by finding the limit as z approaches 10 from the left. lim_ f(z): z+10 Next we need to find the limit as z approaches 10 from the right. > lim_ f(x)= z+10+ c= Now we need to find the value of c that will ensure the left limit is equal to the right limit. So, we set the one-sided limits equal to each other and solve for c. With the correct value of c, we have lim f(x)= lim f(x). This means that the two-sided limit exists z+10 2-10 and lim f(x) = f(10). Consequently, f is continuous at 10 and therefore continuous on (-00, 00)." -10 Question Help:Video Submit Question

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