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Find the following limits algebraically or explain why they don’t exist. lim x>0 sin5x/2x lim x>0 1cosx/x lim x>7 x7/x7 lim x>7 (/x+2)3/x7 lim h>0 (2+h)^38/h lim t>0 1/t  1/t^2+t 
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(a) By graphing the function f(x) = (cos 2x − cos x)/x2 and zooming in toward the point where the graph crosses the yaxis, estimate the value of lim x → 0 f(x). (b) Check your answer in part (a) by evaluating f(x) for … 
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Note that f is continuous on (−∞, 6) and (6, ∞). For the function to be continuous on (−∞, ∞), we need to ensure that as x approaches 6, the left and right limits match. First we find the left limit. …