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

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

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

If the following function is continuous, what is the value of a + b?ℎ(𝑡)={3𝑡2−2𝑡+1,if 𝑡<0𝑎cos⁡(𝑡)+𝑏,if 0≤𝑡≤𝜋34sin⁡2𝑡,if 𝑡>𝜋3h(t)= ⎩⎨⎧​ 3t 2 −2t+1,acos(t)+b,4sin 2 t,​ if t<0if 0≤t≤ 3π​ if t> 3π​ ​ A.1B.0C.4D.3E.2

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)

A.𝑓(𝑡)=2𝑡−𝑡3f(t)=2 t −t 3 B.𝑑(𝑡)=(1.1)𝑡d(t)=(1.1) t C.𝑏(𝑡)=𝑡4−3𝑡+9b(t)=t 4 −3t+9D.ℎ(𝑡)=5𝑡+𝑡5h(t)=5 t +t 5 E.𝑐(𝑡)=𝑡2−5𝑡c(t)= t 2 −5t​