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Which of the following is NOT a component of the course code for the Calculus I final exam?
Which of the following is NOT a component of the course code for the Calculus I final exam?
The final exam for Calculus I was administered on May 23, 2019.
The final exam for Calculus I was administered on May 23, 2019.
True (A)
What is the department responsible for the Calculus I course?
What is the department responsible for the Calculus I course?
Department of Mathematics and Sciences
The total number of questions on the Calculus I final exam was ______.
The total number of questions on the Calculus I final exam was ______.
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Match the following information with their corresponding details:
Match the following information with their corresponding details:
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Flashcards
Course Code
Course Code
A unique identifier for a specific course.
Course Title
Course Title
The name of the course being taught or studied.
Final Examination
Final Examination
A test to evaluate students' understanding at the end of a term or course.
Total Questions
Total Questions
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Total Marks
Total Marks
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Study Notes
Final Examination Question Paper (Spring 2018-19)
- Course Code: MATH 199
- Course Title: CALCULUS I
- Date of Exam: 23-05-2019
- Time: 09:00-11:00
- Total Questions: 9
- Total Marks: 40
- Question Paper Details: The examination paper consists of five printed pages, including the cover page and the last page. If a page is missing, inform the proctor immediately.
Useful Formulae
- Average Rate of Change: f(x₂)-f(x₁))/(x₂-x₁)
- Derivative of a function: lim (h→0) [f(x+h)-f(x)]/h
- Derivative Formulas:
- d(eu)/dx = eu du/dx
- d(um)/dx = mum-1 du/dx
- d(au)/dx = au ln(a) du/dx
- d(logau)/dx = (1/(u ln(a))) du/dx
- d(sin u)/dx = cos u du/dx
- d(cos u)/dx = -sin u du/dx
Examination Questions
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Question 1: Find the domain of f(x) = √(x-16).
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Question 2: Find the limits of the functions;
- (a) lim x→-1 (3x+5)/2
- (b) lim x→2 (x²-7x+10)
- (c) lim x→0 (5x⁴+4-2)/x
- (d) lim x→0 (x²-2x+2sin6x)/(2xcos x)
- (e) lim x→∞ (3x²+x²+1) / (x⁵+1)
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Question 3: Given function f(x);
- (a) Find lim x→3⁺ f(x) and lim x→3⁻ f(x)
- (b) Find lim x→3 f(x)
- (c) Find lim x→3 f(x)
- (d) Is f(x) continuous at x = 3? Justify your answer.
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Question 4: Find the average rate of change of f(x)= x²+2x over the interval [-1, 1].
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Question 5:
- (a) Find the derivative of f(x)= 2x²-3 using the definition at x=1.
- (b) Find the equation of the tangent line to the curve at x=1.
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Question 6: Find the first derivative of the following functions:
- (a) f(x) = 4(2x²+1)
- (b) f(x) = sin(3x³ + 2x)
- (c) f(x) = e(x² sin x)
- (d) f(x) = ln(x² + 3x² + 2x)
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Question 7: Find dy/dx of xy + y² = 1 using implicit differentiation.
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Question 8: Find dy/dx of y = (sin x)x using logarithmic differentiation.
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Question 9: Given f(x)=x³+3x²-18x+2;
- (a) Find the critical points of f(x).
- (b) Find the intervals where f(x) is increasing or decreasing.
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Description
Prepare for your Calculus I final exam with this comprehensive question paper from Spring 2018-19. It covers essential topics including rates of change, derivatives, and limit problems. Get ready to tackle 9 challenging questions worth a total of 40 marks.
