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- Use the limit definition to compute the derivatives at the given value of a: 1) f(x) = 3x-5/x-2 for a = 1Prove rigorously that lim lxl = 0.x→ 0In this example, we can combine the three simple results following the limit definition with the results in Theorem 1 to calculate the limits. We simply substitute the x- and y-values of the point being approached into the functional expression to find the limiting value.
- Find the slope of the graph of the function g(x) = (5x)/(x-2) at (3,15) using the definition of a limit.Estimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→0 x − 3 x − 1Evaluate the limit limx→5 x^2 − 2x −15 / x−5 Enter I for ∞, −∞ and DNE if the limit does not exist.