Midterm 02 sample practice exam PDF

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Practice Exam 2 for MATH 1337 Pake Melland...

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Math 1337 Calculus I Practice Midterm 2 1 2 3 4 5 6 Total

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1. For the following functions of x (defined explicitly or implicitly), find the derivative with respect to x. ⇣ ⌘ a) f (x) = g xx1

b) x3 + y2 + xy = yx

c) tan−1

⇣p

1 + x2

⌘

1.

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2. For the following functions of x (defined explicitly or implicitly), find the derivative with respect to x. a) y = etan(πx)

  b) f (x) = ln ax2 + bx + c

c) f (x) = eg(ln x) ,

g(·) is a differentiable function

2.

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3. Find the equation of the line tangent to the given curve at the specified point. x2 + y2 + 5 = 4 + 2x + 4y, at (x, y) = (−1, 2)

3.

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4. The hour hand of a clock is 1 inch and the minute hand is 2 inches long. Use the Law of Cosines (illustrated below) to calculate the rate at which the distance between the tip of the hour hand and the tip of the minute hand is changing at 2 pm. (Express your answer in inches per minute).

5. Use a linear approximation to estimate the given function at the provided point. f (x) = 2x2 + 4x + 1; at x = 1.1

5.

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6. Find the local and/or absolute maxima for the function over the specified domain.  2 y = x − x2 over [−1, 1]

(over −1 ≤ x ≤ 1)

6.

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