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Let L(c) be the length of the parabola f(x)=x² from x = 0 to x=c, where c20 is a constant. a. Find an expression for L and graph the function. b. Is L concave up or concave down on [0,00)? c. Show that as c becomes large and positive, the arc length function increases as c²; that is L(c) kc², where k is a constant.

Let L(c) be the length of the parabola f(x)=x² from x = 0 to x=c, where c20 is a constant. a. Find an expression for L and graph the function. b. Is L concave up or concave down on [0,00)? c. Show that as c becomes large and positive, the arc length function increases as c²; that is L(c) kc², where k is a constant.

Intermediate Algebra
Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Conic Sections
Section8.2: More Parabolas And Some Circles
Problem 63.1PS
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Let L(c) be the length of the parabola f(x)=x² from x=0 to x = c, where c≥0 is a constant. a. Find an expression for L and graph the function. b. Is L concave up or concave down on [0,00)? c. Show that as c becomes large and positive, the arc length function increases as c²; that is L(c) kc², where k is a constant. C a. What is the expression for L(c)? O A. L(c) = c+ c³ 1 O B. L(c) = = = = c√/₁+4c² + = = In (2c + √/₁1 +4c²) O C. L(c) = = 3/0³ 1 O D. L(c) = c) = (1 + 2c) ³/²2 - Choose the correct graph of L(c) below. O A. O B. Ay Q Ay 20+ 20+ Q Q ✔ b. Is L concave up or concave down on [0,00)? O A. L has regions that are both concave up and concave down on [0,00). O B. L is concave down on [0,00). O C. L is concave up on [0,00). c. If L(c) ~ kc² for large positive values of c, then what must be true? L(c) O A. must approach one as c approaches ∞. c² L(c) O B. must approach a finite value as c approaches ∞. c² L(c) O C. must approach zero as c approaches co. c² L(c) Evaluate the limit as c approaches ∞o. L(c) lim c→ ∞ Therefore, the limit of L(c) c² meets the condition for L(c) kc². O C. Ay 20- 0- 0 ✔ O D. Ay 20- 0- 0 ✔
Transcribed Image Text:Let L(c) be the length of the parabola f(x)=x² from x=0 to x = c, where c≥0 is a constant. a. Find an expression for L and graph the function. b. Is L concave up or concave down on [0,00)? c. Show that as c becomes large and positive, the arc length function increases as c²; that is L(c) kc², where k is a constant. C a. What is the expression for L(c)? O A. L(c) = c+ c³ 1 O B. L(c) = = = = c√/₁+4c² + = = In (2c + √/₁1 +4c²) O C. L(c) = = 3/0³ 1 O D. L(c) = c) = (1 + 2c) ³/²2 - Choose the correct graph of L(c) below. O A. O B. Ay Q Ay 20+ 20+ Q Q ✔ b. Is L concave up or concave down on [0,00)? O A. L has regions that are both concave up and concave down on [0,00). O B. L is concave down on [0,00). O C. L is concave up on [0,00). c. If L(c) ~ kc² for large positive values of c, then what must be true? L(c) O A. must approach one as c approaches ∞. c² L(c) O B. must approach a finite value as c approaches ∞. c² L(c) O C. must approach zero as c approaches co. c² L(c) Evaluate the limit as c approaches ∞o. L(c) lim c→ ∞ Therefore, the limit of L(c) c² meets the condition for L(c) kc². O C. Ay 20- 0- 0 ✔ O D. Ay 20- 0- 0 ✔
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