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
Key points of this exam paper are: Tangent, Curve, Point, Limit Definition, Evaluate, Maximum Value, Minimum Values, Solution, Unique, Increasing
Typology: Exams
1 / 4
This page cannot be seen from the preview
Don't miss anything!
Math 105 C Balcomb Exam 2 November 7, 2008
1 (15). Find the derivative for each of the following:
a) g(x) = 2 x^3 + 5
b) h(x) = arcsin(5x)
c) f(x) = ln(x e2x)
2.(10) Find an equation of the tangent line to the graph x^2 + 2y^2 = 3 at the point (1,1).
3.(15) Evaluate the following limits:
a. lim sin(x) โ x xโ 0 x^3
b) lim ex xโโ ln(x)
c) lim axm^ + 2 if m < n xโโ bxn^ โ 1
4.(10) Find an antiderivative of f(x) = (^9) x^2
5.(10) Find tan(arcsin(x)) rewritten as a algebraic expression.
8.(10) Consider the region in the xy-plane bounded above by the graph of y = 4 โ x^2 and below by the x-axis. Find the dimensions of the rectangle in this region with the largest area. Justify your answer using calculus.
9.(5) Find (f -1)โฒ(12) for the function f(x) = 2 3
x +^ x โ.
