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- Compute the lim(x,y)->(0,0) (4x2y)/(x2+y2)1/2Suppose f(x) = x2 if x ̸= 2 and is undefined at x = 2. The domain is (−∞,2)∪(2,∞). Find lim f (x). x→2Let 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.
- If √5 − 2x^2 ≤ g(x) ≤ √5 − x^2 for −1 ≤ x ≤ 1, find limx→0g(x)Evaluate the following: 1. lim √(6-y) - 2 y-> 2- y2 - 4 y + 4 2. lim |2t-1| - |2t+1| t-> 0- |t|3. lim ( v2 [[v]] - |v-4| ) v-> 2-4. lim [[x]] - |x| x-> 0+ [[x]] + 1Consider the function f(x)=(x4 -2x3)/(x-2). Verify that Lim (x->2) f(x)=8. In order to guarantee that the values of f(x) are within 0.4 units of 8, how close must the x values be to 2? Don’t round your answer; be exact.