Il Maraschini-Palma - volume 5

My English lesson THEOREM (continuity at a point) y A function is continuous at the point a if and only if: lim f(a + x ) f(a) = 0 f (a + x) x 0 f (a) O x a a + x x The theorem expresses a way of looking at continuity in intuitive terms: the function is continuous at a if, as it approaches a on the x-axis, its value tends to approach f(a) on the y-axis. EXERCISES FILL IN THE GAPS 1. A function y = f(x) is continuous at a point a R if it is defined at the point ......................... and its ........................., as ......................... tends to ........................., coincides with the value of the ......................... at a. 2. A function is said to be continuous in an interval if it is ......................... at ......................... of its .......................... 3. If y = f(x) and y = g(x) are two continuous ......................... ......................... at the point a, then the function f(x) + ......................... is at the point a. f(x) 4. If y = f(x) and y = g(x) are two continuous ......................... at the point a, then the function _ is ......................... at the g(x) point ......................... if a ......................... a zero for the function ......................... TEST 5. The function y = 1 _____ x+2 {x2 if x < 1 if x 1 a. is continuous in x = 1 V F a. continuous V F b. discontinuous in x = 1, x = 1 e x = 2 3 c. continuous in ( 3 ; _) 2 d. with a discontinuity that can be eliminated in x = 2 V F V F V F b. is continuous in x = 2 V F V F b. is continuous in x = 1 V F c. presents a discontinuity in x = 1 V F 6. The side graph represents a function y 1 1O 1 1 x x2 £ 7. The function y = _ x+1 a. presents a discontinuity that can be eliminated in x = 1 8. The graph below represents a function 2 172 1 y a. continuous V F 1 b. discontinuous in x = 1 V F c. continuous in x = 0 V F d. with a discontinuity that can be eliminated in x = 1 V F O 1 2 x

Il Maraschini-Palma - volume 5
Il Maraschini-Palma - volume 5