Suppose fÝxÞ = ßsinÝx 2 ? 4Þà ?1 . Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite (essential), or jump discontinuities. (3 Points)
Question
Suppose fÝxÞ = ßsinÝx 2 ? 4Þà ?1 . Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite (essential), or jump discontinuities. (3 Points)
Solution
The function given is f(x) = sin(x^2 - 4) - 1.
Step 1: Identify the points of discontinuity The function f(x) = sin(x^2 - 4) - 1 is a composition of continuous functions, namely the sine function and the quadratic function. Therefore, it is continuous everywhere in its domain. The domain of this function is all real numbers, so there are no points of discontinuity.
Step 2: Determine the type of discontinuity Since there are no points of discontinuity, we don't need to classify them as removable, infinite (essential), or jump discontinuities.
So, the function f(x) = sin(x^2 - 4) - 1 is continuous for all real numbers.
Similar Questions
Suppose fÝxÞ = Ýx?1Þ 2 x+1 if x < 2 x 2 ?2x?8 x?4 if 2 ² x < 4 1 x?3 + 5 if 4 ² x . Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite (essential), or jump discontinuities. (4 Points)
.G i v e nfÝxÞ = x 4 +17 6x 2 +x?1 , identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite (essential), or jump discontinuities. (2 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)
ist the value(s) of 𝑥 at which 𝑓 is discontinuous.
Let be some fixed parameter. The following function is discontinuous at .Question 5Select one:TrueFalse
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.