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Math 1131 Exam Solutions, October 4th, 2007, Exams of Analytical Geometry and Calculus

Columbus State University (CSU)Analytical Geometry and Calculus

Solutions to math 1131 exam questions from october 4th, 2007. Finding the equation of the tangent line to a function at a given point, computing derivatives and their domains, determining where two circles intersect and if they are orthogonal, finding nth derivatives, and differentiating various functions. Graphing calculator is recommended for some questions.

Typology: Exams

Pre 2010

Uploaded on 08/04/2009

koofers-user-ci3
koofers-user-ci3 🇺🇸

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Roll No Name:
Test #2, October 4th, 2007
Math 1131
1. Consider the function f(x) = 5−2x
2 + x2. Find the equation of the tangent line to the graph
of y=f(x) at the point (1,1). Use a graphing calculator to draw the graph of y=f(x) and
the above tangent line.
2. Compute the derivative and its domain for each of the following functions:
(a)f(x) = cos3x
sin x(b)g(x) = 3
r2 + x
3x+ 2
(c)h(x) = sin(ln x) (d)i(x) = 3x3ln(x)−x3
9
I
pf3

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Roll No Name: Test # 2, October 4th, 2007 Math 1131

  1. Consider the function f (x) = 5 − 2 x 2 + x^2 . Find the equation of the tangent line to the graph

of y = f (x) at the point (1, 1). Use a graphing calculator to draw the graph of y = f (x) and the above tangent line.

  1. Compute the derivative and its domain for each of the following functions:

(a)f (x) = cos^3 x sin x (b)g(x) = 3

2 + x 3 x + 2

(c)h(x) = sin(ln x) (d)i(x) = 3 x^3 ln(x) − x^3 9

I

  1. Determine the equation of the tangent line to the graph of equation (x + 2y)^3 = 16x^2 y^2 at the point (2, 1).
  2. Show that the circles x^2 + y^2 = 9 and (x − 5)^2 + y^2 = 16 are orthogonal at the points where they intersect: (^95 , 125 ) and (^95 , − 512 ).
  3. Find the nth derivative of f (x) = xe−x.

II