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Unformatted text preview: Name: TA: Math 20A. Midterm Exam 1 October 23, 2008 Sec. No: PID: Sec. Time: Turn oﬀ and put away your cell phone. No calculators or any other electronic devices are allowed during this exam. You may use one page of notes, but no books or other assistance during this exam. Read each question carefully, and answer each question completely. Show all of your work; no credit will be given for unsupported answers. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clariﬁcation. # 1 2 3 4 5 6 Σ Points Score 6 6 9 6 6 6 39 1. Let f (x) = 2 + √ 2 − x. (a) (2 points) Determine the domain and range of f . (b) (4 points) Find a formula for the inverse f −1 (x) and state its domain and range. 2. Let f (t) = 18 . 1 + et (a) (3 points) Find f ′ (t). (b) (3 points) Compute f ′ (ln(2)). The correct value is an integer. 3. Find the following limits: √ 4+h−2 (a) (3 points) lim h→0 h 2 θ2 (b) (3 points) lim θ →0 sin(2θ ) sin(5θ ) (c) (3 points) lim+
x→ π 5 cos(x) x−π 4. (6 points) Use the intermediate value theorem to show that there is at least one negative real number x satisfying the equation x3 − x + 1 = 0. 5. Let g be a function such that g (1) = 2 and g ′ (1) = −5. (a) (3 points) Find an equation for the line tangent to the graph of g at the point (1, 2). (b) (3 points) Find the value of lim g (x) − g (1) and justify your answer. x→ 1 x−1 6. (6 points) Find the rate of change of the volume V of a cube with respect to its surface area A. ...
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 Fall '08
 Eggers
 Math

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