Question

For what value of the constant c is the function f continuous on (-∞, ∞)? f(x) = cx^2 + 3x if x < 4 x^3 - cx if x ≥ 4 Note that f is continuous on (-∞, 4) and (4, ∞). For the function to be continuous on (-∞, ∞), we need to ensure that as x approaches 4, the left and right limits match. First, we find the left limit. lim x→4- f(x) = lim x→4- (cx^2 + 3x) = 16c + 12 Next, we find the right limit. lim x→4+ f(x) = lim x→4+ (x^3 - cx) = _________

Name: for what value of the constant c is the function f continuous on fx cx2 3x if x 4 x3 cx if x 4 note that f is continuous on 4 and 4 for the function to be continuous on we need to ensure tha 28515
Uploaded: 2023-02-22T12:58:24-08:00
Duration: 1 min 53 s
Channel: Donna Densmore
Description: for what value of the constant c is the function f continuous on fx cx2 3x if x 4 x3 cx if x 4 note that f is continuous on 4 and 4 for the function to be continuous on we need to ensure tha 28515

          For what value of the constant c is the function f continuous on (-∞, ∞)?

f(x) =  
cx^2 + 3x if x < 4
x^3 - cx if x ≥ 4

Note that f is continuous on (-∞, 4) and (4, ∞). For the function to be continuous on (-∞, ∞), we need to ensure that as x approaches 4, the left and right limits match.

First, we find the left limit.
lim x→4- f(x) = lim x→4- (cx^2 + 3x) = 16c + 12
  
Next, we find the right limit.
lim x→4+ f(x) = lim x→4+ (x^3 - cx) = _________

Added by Gabriel T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Donna Densmore

02/22/2023

Step 1

lim x→4− f(x) = lim x→4− (cx^2 + 3x) = 16c + 12 Show more…

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For what value of the constant c is the function f continuous on (-∞, ∞)? f(x) = cx^2 + 3x if x < 4 x^3 - cx if x ≥ 4 Note that f is continuous on (-∞, 4) and (4, ∞). For the function to be continuous on (-∞, ∞), we need to ensure that as x approaches 4, the left and right limits match. First, we find the left limit. lim x→4- f(x) = lim x→4- (cx^2 + 3x) = 16c + 12 Next, we find the right limit. lim x→4+ f(x) = lim x→4+ (x^3 - cx) = _________