Q17) The slope of the tangent line of the curve x² + y²=5 at the point (1,-2)- A) √√4x-4-√√5x-1 x-3 Q18) if f(x)=- x=3 15) Cie D) 2 Tx 5/2 E 11) 112 Di and if f(x) is continuous everywhere. Find the value for
Q17) The slope of the tangent line of the curve x² + y²=5 at the point (1,-2)- A) √√4x-4-√√5x-1 x-3 Q18) if f(x)=- x=3 15) Cie D) 2 Tx 5/2 E 11) 112 Di and if f(x) is continuous everywhere. Find the value for
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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please solve question 17 and 18
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### Educational Website - Calculus Practice Problems
#### Problem 14:
\[ \int_{3}^{5} 2x^2(1 + x^2)^{10} \, dx \]
Choices:
- A) \( (1 - x^2)^9 \bigg|_3^5 \)
- B) \( \frac{(1 + x^2)^11}{10} \bigg|_3^ 5 \)
- C) \( \frac{(1 + x^2)^10}{10} \bigg|_3^5 \)
- D) \( (1 + x^2)^9 \bigg|_3^ 5 \)
#### Problem 15:
Given \( f(x) = x + \cos x \), \( x \in [0, \pi] \). Determine:
1. \( f \) has an inflection point at \( x \) if __.
2. \( f \) has a stationary point at \( x \) if __.
3. \( f \) has a maximum point at \( x \) if __.
#### Problem 16:
Find the value for \( a, b \), if \( x(t)= e^{2t} cos t + 4t^2 + bx \) has maximum point as \( t = 0 \) and inflection point at \( t = 1 \).
Choices:
- A) a = -2, b = 20
- B) a = -2, b = 20
- C) a = -2, b = 20
- D) a = -2, b = 20
#### Problem 17:
The slope of the tangent line of the curve \( x^2 + y^2 = 5 \) at the point \((1, 1)\):
- A) \( \frac{-1}{2} \)
- B) \( \frac{1}{1} \)
- C) \( -1 \)
- D) \( 1 \)
#### Problem 18:
If \( f(x) = \sqrt{4x + 5x + 1} \) when \( x \ne 3 \) and \( f(x) = k \) is continuous everywhere. Find the value for \( k \).
Choices:
- A) \( \frac{-1}{8} \)
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F020957b5-d477-4d69-ba0e-6d5c169d47a8%2F59a7136c-0e16-42b7-9c36-f099b8d22d17%2Ffxj5fts_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Educational Website - Calculus Practice Problems
#### Problem 14:
\[ \int_{3}^{5} 2x^2(1 + x^2)^{10} \, dx \]
Choices:
- A) \( (1 - x^2)^9 \bigg|_3^5 \)
- B) \( \frac{(1 + x^2)^11}{10} \bigg|_3^ 5 \)
- C) \( \frac{(1 + x^2)^10}{10} \bigg|_3^5 \)
- D) \( (1 + x^2)^9 \bigg|_3^ 5 \)
#### Problem 15:
Given \( f(x) = x + \cos x \), \( x \in [0, \pi] \). Determine:
1. \( f \) has an inflection point at \( x \) if __.
2. \( f \) has a stationary point at \( x \) if __.
3. \( f \) has a maximum point at \( x \) if __.
#### Problem 16:
Find the value for \( a, b \), if \( x(t)= e^{2t} cos t + 4t^2 + bx \) has maximum point as \( t = 0 \) and inflection point at \( t = 1 \).
Choices:
- A) a = -2, b = 20
- B) a = -2, b = 20
- C) a = -2, b = 20
- D) a = -2, b = 20
#### Problem 17:
The slope of the tangent line of the curve \( x^2 + y^2 = 5 \) at the point \((1, 1)\):
- A) \( \frac{-1}{2} \)
- B) \( \frac{1}{1} \)
- C) \( -1 \)
- D) \( 1 \)
#### Problem 18:
If \( f(x) = \sqrt{4x + 5x + 1} \) when \( x \ne 3 \) and \( f(x) = k \) is continuous everywhere. Find the value for \( k \).
Choices:
- A) \( \frac{-1}{8} \)
-
![### Calculus and Functions Practice Problems
#### Q14) Evaluate the integral:
\[ 2x^3(1 + x^2)^{-1} dx \]
\[ A) \frac{(1+ x^2)^{10}}{10} \quad B) \frac{(1 + x^2)^{10}}{11} \quad C) \frac{(1 + x^2)^9}{9} \]
---
#### Q15) If \( f(x) = x + \cos x, \; x \in [0, \pi] \), then the function has an inflection point at:
\[ A) x = 0, \; b = 20 \quad B) a = 2, \; b = -20 \]
---
#### Q16) Find the value for \( a, b \) if \( f(x) = \sqrt{4x^2 + bx + a} \) has stationary point at \( -2 \), and point of inflection at \( -4 \).
\[ A) a = 2, \; b = 20 \quad B) a = 2, \; b = -20 \]
---
#### Q17) The slope of the tangent line of the curve \( x^3 + y^2 = 5 \) at the point \( (-2, 9) \) is:
\[ A) 1 \quad B) 1 \quad C) 0 \quad D) -1 \]
---
#### Q18) If \( f(x) = \frac{\sqrt{4x + 4 - \sqrt{5x + 1}}}{x - 3} \) and \( f(x) \) is continuous everywhere. Find the value \( k \).
\[ \text{A) } -\frac{1}{8} \quad \text{B) } 1 \quad \text{C) } 0 \quad \text{D) } \]
---
#### Q19) Use local linear approximation to find an approximation value for \( \sqrt{8.9} \):
\[ A) \frac{300}{80} \quad B) \frac{319}{80} \]
---
#### Q20) If the graph of the function \( f(x) \) is stretched vertically by a factor 2 and then translated 4 units left,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F020957b5-d477-4d69-ba0e-6d5c169d47a8%2F59a7136c-0e16-42b7-9c36-f099b8d22d17%2F8wuj3k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculus and Functions Practice Problems
#### Q14) Evaluate the integral:
\[ 2x^3(1 + x^2)^{-1} dx \]
\[ A) \frac{(1+ x^2)^{10}}{10} \quad B) \frac{(1 + x^2)^{10}}{11} \quad C) \frac{(1 + x^2)^9}{9} \]
---
#### Q15) If \( f(x) = x + \cos x, \; x \in [0, \pi] \), then the function has an inflection point at:
\[ A) x = 0, \; b = 20 \quad B) a = 2, \; b = -20 \]
---
#### Q16) Find the value for \( a, b \) if \( f(x) = \sqrt{4x^2 + bx + a} \) has stationary point at \( -2 \), and point of inflection at \( -4 \).
\[ A) a = 2, \; b = 20 \quad B) a = 2, \; b = -20 \]
---
#### Q17) The slope of the tangent line of the curve \( x^3 + y^2 = 5 \) at the point \( (-2, 9) \) is:
\[ A) 1 \quad B) 1 \quad C) 0 \quad D) -1 \]
---
#### Q18) If \( f(x) = \frac{\sqrt{4x + 4 - \sqrt{5x + 1}}}{x - 3} \) and \( f(x) \) is continuous everywhere. Find the value \( k \).
\[ \text{A) } -\frac{1}{8} \quad \text{B) } 1 \quad \text{C) } 0 \quad \text{D) } \]
---
#### Q19) Use local linear approximation to find an approximation value for \( \sqrt{8.9} \):
\[ A) \frac{300}{80} \quad B) \frac{319}{80} \]
---
#### Q20) If the graph of the function \( f(x) \) is stretched vertically by a factor 2 and then translated 4 units left,
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