Provide an appropriate response. Is the function given by f(x) = 32 x + 4 contin

Question

Provide an appropriate response. Is the function given by f(x) = 32 x + 4 continuous at x = 4? Why or why not? Is the function given by f(x) = squareroot 2x + 5 continuous at x = -5/2? Why or why not? Determine where the function H(x) = x^2 + 7/x62 + x - 6 is continuous. Determine the points at which the function is discontinuous. h(x) = {x^2 - 4 for x 1 Solve the problem. A car's distance in miles from its starting point after t hours is given by s(t) = 6t^2 Find the average rate of change of distance with respect to time (average velocity) as t changes from t_1 = 4 to t_2 = 6. Suppose that the dollar cost of producing x radius is c(x) = 400 + 20 x - 0.2 x^2. Find the average cost per radio of producing the first 45 radios.

Explanation / Answer

(12) f(x) = 32x + 4

Limit (x -> 4-) of 32x + 4 = 32(4) + 4 = 132

f(4) = 32(4) + 4 = 132

Limit (x -> 4+) of 32x + 4 = 32(4) + 4 = 132

Since all the three limits are equal, f(x) is continuous at x = 4

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