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Practice Exam 2 - Spring 2005 - Calculus and Analytic Geometry I | MAT 250, Exams of Analytical Geometry and Calculus

Material Type: Exam; Class: Calculus and Analytical Geometry I; Subject: MAT Mathematics; University: Murray State University; Term: Unknown 1989;

Typology: Exams

Pre 2010

Uploaded on 08/16/2009

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koofers-user-qn7 🇺🇸

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Spring ’05/MAT 250/Exam 2 Name: Show all your work.
Differentiate and simplify where appropriate:
1. (4pts) d
dx (7x34x+3
x2+c4) =
2. (4pts) d
dx (xln xx) =
3. (5pts) d
dx cos x25x+ 10 =
4. (5pts) d
dx
x
x2+ 5 =
pf3
pf4

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Spring ’05/MAT 250/Exam 2 Name: Show all your work.

Differentiate and simplify where appropriate:

  1. (4pts)

d dx

(7x^3 − 4 x^ + 3

x^2 + c^4 ) =

  1. (4pts)

d dx

(x ln x − x) =

  1. (5pts)

d dx

cos

x^2 − 5 x + 10 =

  1. (5pts)

d dx

x √ x^2 + 5

  1. (5pts) Use logarithmic differentiation to find

d dx

xtan^ x.

  1. (4pts) Find the first three derivatives of f (x) and use them to find the formula for f (n)(x) if f (x) = ex(x + 5).
  2. (6pts) Use implicit differentiation to find y′.

exy^ = x^2 + y^4

  1. (7pts) A plane flying horizontally at an altitude of 1mi and a speed of 500mi/hr passes directly over a radar station. Find the rate at which the straight-line distance from the plane to the radar station is increasing when this distance is 2mi.

Bonus. (5pts) Verify that

d dx

2 x^2 − 1 4

arcsin x +

x

1 − x^2 4

= x arcsin x.