dx 19) u = 4x + 9 4x +9 1 A) B) 2/4x + 9 + C + C + 9)3/2 1 + C V4x + 9 C) 2- S dx 20) u == 4x + 6 4x + 6 1 A) 4(4x + 6)3/2 B) 2/4x + 6 + C + C 1 |4x + 6 + C D) 2– + C V4x + 6 Solve the initial value problem. 21) dy (2x2), y(0) = 11 = x COS A) y = u sin (u) B) y = sin (2x2) + + 11 C) y = sin(2x2) + 11 - sin(2x2) + 11 2 D) y =
dx 19) u = 4x + 9 4x +9 1 A) B) 2/4x + 9 + C + C + 9)3/2 1 + C V4x + 9 C) 2- S dx 20) u == 4x + 6 4x + 6 1 A) 4(4x + 6)3/2 B) 2/4x + 6 + C + C 1 |4x + 6 + C D) 2– + C V4x + 6 Solve the initial value problem. 21) dy (2x2), y(0) = 11 = x COS A) y = u sin (u) B) y = sin (2x2) + + 11 C) y = sin(2x2) + 11 - sin(2x2) + 11 2 D) y =
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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Question
![### Calculus Problems and Solutions
#### Integration Problems:
**19) Solve the integral:**
\[
\int \frac{dx}{\sqrt{4x+9}}, \quad u = 4x + 9
\]
Options:
- A) \(\frac{1}{4(4x+9)^{3/2}} + C\)
- B) \(2\sqrt{4x+9} + C\)
- C) \(\frac{1}{\sqrt{4x+9}} + C\)
- D) \(\frac{1}{2\sqrt{4x+9}} + C\)
**20) Solve the integral:**
\[
\int \frac{dx}{\sqrt{4x+6}}, \quad u = 4x + 6
\]
Options:
- A) \(\frac{1}{4(4x+6)^{3/2}} + C\)
- B) \(2\sqrt{4x+6} + C\)
- C) \(\frac{1}{\sqrt{4x+6}} + C\)
- D) \(\frac{1}{2\sqrt{4x+6}} + C\)
#### Differential Equations:
**21) Solve the initial value problem:**
\[
\frac{dy}{dx} = x \cos(2x^2), \quad y(0) = 11
\]
Options:
- A) \(y = \frac{1}{u} \sin(u)\)
- B) \(y = \sin(2x^2) + 11\)
- C) \(y = \frac{1}{4} \sin(2x^2) + 11\)
- D) \(y = \frac{x^2}{2} \sin(2x^2) + 11\)
**22) Solve the initial value problem:**
\[
\frac{dy}{dx} = 18(6x-2)^{-4}, \quad y(0) = 1
\]
Options:
- A) \(y = -\frac{3}{5}(6x-2)^{-5} + 0.981\)
- B) \(y = - (6x-2)^{-3} + 0.875\)
- C) \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d35f65e-f33f-4a8a-9781-3db59b6770a0%2F02f6c492-3d72-461a-b7cb-91f39c86009a%2Fdyiyvjr_processed.png&w=3840&q=75)
Transcribed Image Text:### Calculus Problems and Solutions
#### Integration Problems:
**19) Solve the integral:**
\[
\int \frac{dx}{\sqrt{4x+9}}, \quad u = 4x + 9
\]
Options:
- A) \(\frac{1}{4(4x+9)^{3/2}} + C\)
- B) \(2\sqrt{4x+9} + C\)
- C) \(\frac{1}{\sqrt{4x+9}} + C\)
- D) \(\frac{1}{2\sqrt{4x+9}} + C\)
**20) Solve the integral:**
\[
\int \frac{dx}{\sqrt{4x+6}}, \quad u = 4x + 6
\]
Options:
- A) \(\frac{1}{4(4x+6)^{3/2}} + C\)
- B) \(2\sqrt{4x+6} + C\)
- C) \(\frac{1}{\sqrt{4x+6}} + C\)
- D) \(\frac{1}{2\sqrt{4x+6}} + C\)
#### Differential Equations:
**21) Solve the initial value problem:**
\[
\frac{dy}{dx} = x \cos(2x^2), \quad y(0) = 11
\]
Options:
- A) \(y = \frac{1}{u} \sin(u)\)
- B) \(y = \sin(2x^2) + 11\)
- C) \(y = \frac{1}{4} \sin(2x^2) + 11\)
- D) \(y = \frac{x^2}{2} \sin(2x^2) + 11\)
**22) Solve the initial value problem:**
\[
\frac{dy}{dx} = 18(6x-2)^{-4}, \quad y(0) = 1
\]
Options:
- A) \(y = -\frac{3}{5}(6x-2)^{-5} + 0.981\)
- B) \(y = - (6x-2)^{-3} + 0.875\)
- C) \(
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