Chapter 7.5, Problem 7QR

State three part definition of continuity

e2h-1 if f'(a) lim-0 what is f(r) and what is a? h

Use the Squeeze Theorem to show that lim x² cos(207TX) = 0. X → 0 Illustrate by graphing the functions f(x) = -x², g(x) = x² cos(207x), and h(x) = x² on the same screen. Let f(x) = -x², g(x) = x² cos(207tx), and h(x) = x². Then [0 ✓≤ cos(207TX) ≤ 1 f(x) V ≤ x² cos(207Tx) ≤ ? S . Since lim f(x) = lim_h(x) : = X → 0 X → 0 , by the Squeeze Theorem we have lim g(x) X → 0 =

Show a detailed way on how it became indeterminate form

2. By drawing a graph illustrate an example of a function f(x) such that it satisfies these three conditions: lim,→1- = 2, lim,→1+ = -1 and f(1) = 0.

(M1.4 C) Consider the two functions 22+x-2 h(x) and 22 +40+4 k(x) = 2 +x-2 Compute the lim h(x) and_lim_k(x). r-2 Explain why your answers make sense, given that the two functions are reciprocals of each other.

2. Consider the function: x² +3 if x 2 17 if x = 2. Find lim, 42 f (x).

5X²+1 IF X<\ Let F(X) = {(x-2) IF XZ1 a, Find Limx→ 1¹ and lim x→# f(x) b. does Lim X→1 f(x) exist? C. Sketch the graph of f

Find the value of the expression limx→3 (-x2+x+2/x-1)