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The instructions and questions for a university-level mathematics midterm exam. It covers topics such as limits, derivatives, and velocity. Students are required to provide reasoning for their answers and are not allowed to use graphing calculators.
Typology: Exams
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lim x→ 0 +
x − x √ x
Answer
h(t) = 20t − 4. 9 t^2.
a) (3 marks) Using any method you like, find an expression for the velocity of the ball at time t.
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b) (2 marks) At what times is the velocity 0?
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c) (2 marks) What is the maximum height the ball gets above the ground? Clearly explain your answer.
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5a) (1 mark) Find a positive value for δ such that the following statement is true:
If |x| < δ then x^2 < 0 .04.
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b) (1 mark) Write down the precise “ − δ ” definition of
xlim→a f^ (x) =^ L.
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c) (4 marks) Using the definition in part b), prove that
lim x→ 1 (x^2 − 1) = 0.
Answer
Do not write below this line