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1 Compute / - dx, expressing the result in terms of r. 3/2 (36— х?) (Express numbers in exact form. Use symbolic notation and fractions where needed.) 1 dx = 3/2 (36 – x²)*2 Calculate the sided limit to determine what happens to the definite integral as r approaches 6 from the left. (Express numbers in exact form. Use symbolic notation and fractions where nceded. Enter DNE if the limit does not exist.) 1 lim dx = (36 — х2)32

1 Compute / - dx, expressing the result in terms of r. 3/2 (36— х?) (Express numbers in exact form. Use symbolic notation and fractions where needed.) 1 dx = 3/2 (36 – x²)*2 Calculate the sided limit to determine what happens to the definite integral as r approaches 6 from the left. (Express numbers in exact form. Use symbolic notation and fractions where nceded. Enter DNE if the limit does not exist.) 1 lim dx = (36 — х2)32

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Integration and Limit Calculation #### Problem 1: Definite Integral in Terms of \( r \) **Objective:** Compute the integral \(\int_{0}^{r} \frac{1}{(36-x^2)^{3/2}} \, dx\), expressing the result in terms of \( r \). **Instructions:** Express numbers in exact form. Use symbolic notation and fractions where needed. \[ \int_{0}^{r} \frac{1}{(36-x^2)^{3/2}} \, dx = \quad \boxed{} \] #### Problem 2: Limit as \( r \) Approaches 6 **Objective:** Calculate the sided limit to determine what happens to the definite integral as \( r \) approaches 6 from the left. **Instructions:** Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if the limit does not exist. \[ \lim_{r \to 6^-} \int_{0}^{r} \frac{1}{(36-x^2)^{3/2}} \, dx = \quad \boxed{} \]
Transcribed Image Text:### Integration and Limit Calculation #### Problem 1: Definite Integral in Terms of \( r \) **Objective:** Compute the integral \(\int_{0}^{r} \frac{1}{(36-x^2)^{3/2}} \, dx\), expressing the result in terms of \( r \). **Instructions:** Express numbers in exact form. Use symbolic notation and fractions where needed. \[ \int_{0}^{r} \frac{1}{(36-x^2)^{3/2}} \, dx = \quad \boxed{} \] #### Problem 2: Limit as \( r \) Approaches 6 **Objective:** Calculate the sided limit to determine what happens to the definite integral as \( r \) approaches 6 from the left. **Instructions:** Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if the limit does not exist. \[ \lim_{r \to 6^-} \int_{0}^{r} \frac{1}{(36-x^2)^{3/2}} \, dx = \quad \boxed{} \]
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