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- Find the constant c so that the limit limx->3 (x2+x+c)/(x2-5x+6) exists.Find limx∞ h(x), if it exists, f(x) = 5x3 − 3 (a) h(x) = f(x)/x2 (b) h(x) = f(x)/x3 (c) h(x) = f(x) /x4The graph of f(x) = 2x2/(x2 + 2) is shown. (a) Find L = limx ∞ f(x). (b) Determine x1 and x2 in terms of ε. (c) Determine M, where M > 0, such that ∣ f(x) − L∣ < ε for x > M. (d) Determine N, where N < 0, such that ∣ f(x) − L∣ < ε for x < N.
- Let ƒ(x) = (x^2 - 9)/(x + 3). a. Make a table of the values of ƒ at the points x = -3.1, -3.01, -3.001, and so on as far as your calculator can go. Then estimate limxS -3 ƒ(x). What estimate do you arrive at if you evaluate ƒ at x = -2.9, -2.99, -2.999,c instead? b. Support your conclusions in part (a) by graphing ƒ near c = -3 and using Zoom and Trace to estimate y-values on the graph as xS -3. c. Find limxS -3 ƒ(x) algebraically.Given limx→4f(x)=4limx→4f(x)=4 and limx→4g(x)=4limx→4g(x)=4, Evaluate : limx→4f(x)+g(x)8f(x). The Limit is ?Is there a value of a for which limx1 3x^2+ax+a+3/x^2+x-2 exists? Enter the value of a if such a exist otherwise enter 0.
- Let ƒ(x) = (x2 - 9)/(x + 3). Make a table of the values of ƒ at the points x = -3.1,-3.01, -3.001, and so on as far as your calculator can go.Then estimate limx→ -3 ƒ(x). What estimate do you arrive at ifyou evaluate ƒ at x = -2.9, -2.99, -2.999,c instead?Let ƒ(x) = (x2 - 9)/(x + 3). a. Make a table of the values of ƒ at the points x = -3.1, -3.01, -3.001, and so on as far as your calculator can go. Then estimate limx--> -3 ƒ(x). What estimate do you arrive at if you evaluate ƒ at x = -2.9, -2.99, -2.999,...... instead? b. Support your conclusions in part (a) by graphing ƒ near c = -3 and using Zoom and Trace to estimate y-values on the graph as x -->-3.Find the limit. lim x2+5/5x3-2 x→+∞