6.G i v e ngÝxÞ = x 3 ?2x+2 if x ²? 2 x 2 +ax+bi f ?2 < x < 1 4x 4 ?3x 3 ?5x+2 if 1 ² x , find values for a and b so that the function is continuous for all x. (4 Points)

Calculus AB Assignment Continuity Problems 4. Suppose fÝxÞ = x?1 x 4 ?1 if x ² 2 |x?3| x?3 if 2 < x . Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite (essential), or jump discontinuities. (6 Points) 5. Find all the constants a that make the function fÝxÞ = 3Ýa?xÞ if x < 3 a 2 ?x 2 if x ³ 3 continuous for all x. (2 Points) 6.G i v e ngÝxÞ = x 3 ?2x+2 if x ²? 2 x 2 +ax+bi f ?2 < x < 1 4x 4 ?3x 3 ?5x+2 if 1 ² x , find values for a and b so that the function is continuous for all x. (4 Points)

Find all the constants a that make the function fÝxÞ = 3Ýa?xÞ if x < 3 a 2 ?x 2 if x ³ 3 continuous for all x. (2 Points)

If the following function is continuous, then what is the value of a?ℎ(𝑡)={2𝑡+𝑏𝑖𝑓 𝑡<02cos⁡(𝑡)−3𝑖𝑓 0≤𝑡≤𝜋2𝑎sin⁡(𝑡)+5𝑏𝑖𝑓 𝑡>𝜋2h(t)= ⎩⎪⎨⎪⎧​ 2t+b2cos(t)−3asin(t)+5b​ if t<0if 0≤t≤ 2π​ if t> 2π​ ​ A.1B.ℎ(𝑡)={2𝑡+𝑏𝑖𝑓 𝑡<02cos⁡(𝑡)−3𝑖𝑓 0≤𝑡≤𝜋2𝑎sin⁡(𝑡)+5𝑏𝑖𝑓 𝑡>𝜋2h(t)= ⎩⎪⎨⎪⎧​ 2t+b2cos(t)−3asin(t)+5b​ if t<0if 0≤t≤ 2π​ if t> 2π​ ​ C.4D.0E.2

If the following function is continuous, then what is the value of b?𝑔(𝑡)={2𝑡2+2𝑡−24𝑡−3𝑖𝑓 𝑡≠3𝑏𝑖𝑓 𝑡=3g(t)={ t−32t 2 +2t−24​ b​ if t≠3if t=3​ A.14B.3C.7D.None of theseE.0

Let f (x) be defined by: f (x) = 2x /（3 + x） , x ≤ −2 k(x − 2), −2 < x < 4 2x − 6, x ≥ 4 Which of the following values of k would make f (x) continuous on R? a) k = 2 (b) k = 1 (c) There is no such value for k. (d) k = −1