Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
The november 12, 2010 calculus i exam for professor p. Wong's math105a,c class. The exam covers various calculus topics such as finding derivatives, limits, and critical points. Students are required to explain their work and justify their answers.
Typology: Exams
1 / 7
This page cannot be seen from the preview
Don't miss anything!
EXAM II - NOVEMBER 12, 2010
Instruction: Read each question carefully. Explain ALL your work and give reasons to support your answers.
Advice: DON’T spend too much time on a single problem.
Problems Maximum Score Your Score
Total 100
1
1.(15 pts.) Let r(x) be a function with the property that r(0) = 2 and r′(0) = −1.
(i) Suppose f (x) = r(x) sin x. Find f ′(0).
(ii) Suppose g(x) = e
x r(x). Find^ g
(iii) Suppose h(x) = ln(r(x)). Find h′(0).
3.(14 pts.) Consider the curve given by y^2 − 6 xy + 20 = 0.
(i) Find
dy dx.
(ii) Find an equation of the line tangent to the curve at the point (2, 2).
4.(18 pts.) Evaluate each of the following limits (if it exists) algebraically. (Do not evaluate the limits using calculator.) Explain your work.
(i) lim t→∞^3 t
(^2) + t + 1 7 − 5 t − 7 t^2
(ii) lim x→ 12
x (^) − 2 x − 1
(iii) lim θ→ 0 3(1^ − 2 θ^ cos 2 θ)
6.(20 pts.) A rectangle is placed inside the region bounded by the parabola y = 9 − x^2 and the x-axis. [You may assume the bottom of the rectangle is on the x-axis and the upper corners of the rectangle are on the parabola.]
0
A = (x,y)
(a) Suppose the corner (see figure) A has coordinates (x, y). Express the area of the rectangle in terms of x and y.
(b) Find the dimensions of the rectangle which has the maximum area.
