My English lesson EXERCISES FILL IN THE GAPS 1. A function y = f(x), defined at least in the interval [a ; b], and a point x0 ........................., the function f is said to be derivable in .............., if there exists a ......................... limit: f (x 0 .........................) f(.........................) f (x 0) = lim __________________________ ......................... h 2. Link each function to its graph and identify features in each one about continuity and derivability at the indicated points: b. y = |x4 4 x2 1| graph a. y = | 2x + 4| graph y 1 1 O I. ............................... y 1 2 x in ............................... II. 2 O x 1 2 Continuous in ............................... x = 2 ............................... x = 0 ............................... x = 2 ............................... x = 2 ............................... derivable in ............................... x = 2 ............................... x = 0 ............................... derivable in ............................... TEST 10 5x 3. The function y = _: 2x A is continuous but non-derivable in R0 C is non-derivable in x = 2 D is not continuous in x = 0 B is derivable in R 10 5x 4. The function y = _ : 2x A is continuous but non-derivable in R0 | | B is non-derivable in x = 0 and in x = 2 B is derivable in R D is not continuous in x = 0 and in x = 2 5. The function y = |2x x2 1| 6. A is continuous but non-derivable in R B is derivable in R B is non-derivable in x = 1 D is not continuous in x = 1 |2x x2 1| The function y = ___________ (x 1)2 A is continuous but non-derivable in R B is derivable in R B is non-derivable in x = 1 D is not continuous in x = 1 7. The function y = |e x 1| A is continuous but non-derivable in R B is derivable in R B is non-derivable in x = 0 D is not continuous in x = 0 8. The function y = |e x + 1| 278 A is continuous but non-derivable in R B is derivable in R B is non-derivable in x = 0 D is not continuous in x = 0